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#### Rate analysis for M20 concrete Civil Sir

Rate analysis for M20 concrete:- Rate analysis for concrete work summary of all the quantity and cost of material, labours overhead expenses, contractor profit charges and water charges. Rate analysis for concrete is comprise of following:- 1) quantity and cost of material ( cement sand aggregate and water quantity and their cost)

#### Rate Analysis of M20 Concrete|Rate Analysis of Concrete

2021-10-14  In this post, we will learn to do the rate analysis of M20 Concrete. Besides rate estimation, we will also calculate the total amount of material i.e. the number of Cement bags, the quantity of Sand, and the quantity of Coarse Aggregate required to prepare the

#### Rate analysis for M20 concrete CivilEngineerx

2022-1-6  Rate analysis for M20 concrete. Rate analysis of concrete is average an estimate for quotation and billing purpose by mason, supervisor and contractor and for tendering use. Rate Analysis for m20 concrete :- It is a summary of all the cost involved in doing particular work or unit work like material cost, labour cost, overhead expenses, water

#### Rate Analysis for Concrete Excel Reinforced Concrete

2021-12-20  The quantity of materials like cement, sand and coarse aggregates is adjusted as per the mix design, as for instance, M15 (1:2:4), M20 (1:1.5:3), M25, M30 and so on. After that, the rate analysis for 1 m 3 of reinforced concrete should have been worked out. Step 1: Computation of Materials: Materials contain: cement, sand, coarse aggregate and

#### Reinforced Concrete Quantity and Rate Analysis Civil

2017-3-5  The quantity of materials like cement, sand and coarse aggregates change according to the mix design, for example, M15 (1:2:4), M20 (1:1.5:3), M25, M30 and so on. Next, the rate analysis for 1 m 3 of reinforced concrete is to be calculated. Step 1: Estimation of Materials:

#### Rate Analysis of RCC (Reinforcement Cement Concrete)

2022-1-17  In this Rate Analysis of RCC calculation of material, labor, wastage, and other charges in rate analysis. Also, read: Rate Analysis of Brick Masonry Material calculation in Rate Analysis like Cement, sand, aggregate, and reinforcement Cement calculation. Dry Cement volume = 1.25 convert Wet cement.(The concrete mortar dry volume of concrete decrease

#### RATE ANALYSIS OF CONSTRUCTION ITEMS

2014-1-8  New rates of these items can be worked out easily by changing the rates of materials and labours based on current market rates. It is useful for Consultants, Contractors, Architects and Builders for preparing the Rate Analysis of items like Concrete, Brickwork, Plaster etc. Rate analysis of various type of projects like, Buildings, Roads, Bridges,

#### Rate Analysis of M20 Concrete|Rate Analysis of Concrete

2021-10-14  In this post, we will learn to do the rate analysis of M20 Concrete. Besides rate estimation, we will also calculate the total amount of material i.e. the number of Cement bags, the quantity of Sand, and the quantity of Coarse Aggregate required to prepare the

#### Rate analysis of m20 grade concrete henca

2021-8-28  Tariff Analysis for the analysis of the concrete of the concrete M20 average rate is an estimate for the quotation and the purpose of billing mason, supervisor, contractor and for the use of race. Analysis of the rate for the concrete M20: It's a summary of all costs involved in making particular job or work together as material costs, labor

#### Quantity and Rate Analysis for Reinforced Concrete

For rate analysis of RCC, we need to multiply each quantity with their rates to get the amount for every item of work. Rates vary from place to place and time to time. It is advisable to assume local rates or standard rates of the place. The sum total of all the four items above will give the rate or cost for 1m 3 of concrete.

#### Rate Analysis Of Concrete M25 Concrete Example Rate

2022-1-19  Assume We need 1 m3 of wet volume concrete of M25 Mix, (Mix Ratio, M25 = 1: 1 : 2) So Total Parts = 1+1+2 = 4 Parts which gives Dry volume that means before adding water content. Volume of concrete = (1 Cement Part)/4 + (1 Sand Part)/4 + (2 Coarse Aggregate Part)/4. From the IS Code standard, Assuming the water-cement ratio for M20 is 0.5.

#### Reinforced Concrete RCC Rate Analysis Reinforced Steel

2021-2-12  Since the quantity of reinforcement steel varies, labour rates for reinforcement work modifies as per type of structural component. The Quantity of materials similar to sand, cement and coarse aggregates fluctuate with mix design like M15 (1:2:4), M20 (1:1.5:3), M25, M30 etc.. Learn how the rate analysis for 1m 3 of reinforced concrete is done.

#### How many cement bags and sand is required for M20

2020-7-31  For an M20 grade of concrete, the ratio is (1:1.5:3) ie, (1 part of cement: 1.5 part of sand: 3 part of Aggregate) Let us assume for 1 Cum. Of M20 concrete, So, Wet volume of concrete = 1 Cum. Dry volume of concrete = 1.54 times of the wet volume of concrete (Here 1.54 stands. as “Factor of safety” to counter the shrinkage) = 1.54 Cum

2020-7-28  M15 concrete grade concrete gets categorized as an ordinary grade. Its features, properties, and uses are quite close to M10 with a very slight difference.. PROPERTIES OF THE M15 GRADE CONCRETE: It contains a mix ratio is 1:3:6.1 cement .3 sand and six aggregate.M-15 M represents the mix, while 15 N/mm2 is the concrete cube’s characteristic compressive

#### How to do rate Analysis For Concrete? Civil Lead

2022-1-18  So, Rate for 1 cum of M-15 concrete is = 4570.00. Note. Shuttering component is not considered as the quantity of shuttering for the slab, beam, column and foundation shall be different. The material rates considered in this rate analysis are exclusive of GST. The material and labour rates may vary depending on the site condition & type of project.

#### Best Rate Analysis Excel Sheets For Civil Engineering Works

2 天前  Brick Bats Cement Concrete (1:4:8 Ratio) Rate Analysis Excel Sheet RCC slabs sometimes crack and let rainwater through. Therefore, it is important to develop a waterproof roof panel that can provide a leak-proof environment for the interior of the building.

#### ANALYSIS OF RATES OF VARIOUS BUILDING ITEMS.

2017-7-5  RATE ANALYSIS FOR BRICK BAT W/P FOR TOILET. 1. Material cost should include all taxes, such as sales, octroi, excise etc. 2. We have added 5 % as wastage wherever applicable. 3. Rates should include equipments, machineries, temporary approaches, water, fuel & electrical consumptions, contingencies & sundries. 4.

#### Rate Analysis of M20 Concrete|Rate Analysis of Concrete

2021-10-14  In this post, we will learn to do the rate analysis of M20 Concrete. Besides rate estimation, we will also calculate the total amount of material i.e. the number of Cement bags, the quantity of Sand, and the quantity of Coarse Aggregate required to prepare the

#### Rate analysis of m20 grade concrete henca

2021-8-28  Tariff Analysis for the analysis of the concrete of the concrete M20 average rate is an estimate for the quotation and the purpose of billing mason, supervisor, contractor and for the use of race. Analysis of the rate for the concrete M20: It's a summary of all costs involved in making particular job or work together as material costs, labor

#### M20 grade of concrete and their mix ratio CivilEngineerx

2022-1-13  M20 grade of concrete and their mix ratio ,hi guys in this article we know about grade of concrete and m20 grade of concrete mix ratio and ratio of grade of concrete like m5, m 7.5, m10, m15, m 20, m25 and so more.. There are two types of concrete plain cement concrete (PCC) and reinforcement cement concrete (RCC). Plain cement concrete is without use of

#### What will be the cost of M20 grade concrete?/How to

2021-9-29  Estimating cement, sand, & aggregates in 1 CUM. of 1:1.5:3 mix ratio (M20)concrete. A. Material cost: The average ongoing market rate in India is considered for calculation purposes. B. Labor cost : The labor rate for concrete ranges from INR 900/- to 1600/- per CUM. Let us take the average rate of INR 1250/ for the calculation purpose.

#### How to do rate Analysis For Concrete? Civil Lead

2022-1-18  So, Rate for 1 cum of M-15 concrete is = 4570.00. Note. Shuttering component is not considered as the quantity of shuttering for the slab, beam, column and foundation shall be different. The material rates considered in this rate analysis are exclusive of GST. The material and labour rates may vary depending on the site condition & type of project.

#### Carry out the rate analysis for ques10

Carry out the rate analysis for. written 3.3 years ago by sayalibagwe ♦ 9.0k: modified 2.3 years ago by sanketshingote ♦ 740: a) M20 grade R.C.C concrete with 2% steel including formwork and reinforcement. b) Internal Plastering in CM 1:5. {Quantity of cement} \\ = 1.5×2.84 = 4.26m³$Quantity of coarse aggregate$=3 × \text{Quantity

#### Calculate Cement, Sand, And Aggregate Quantity In

2020-9-24  Also Read: Best Civil Engineering Work Rate Analysis Sheets. Quantity in Concrete Work Calculation details: Calculation data: Assume required quantity of concrete is 1m3. Assume concrete grade is M20. Proportion of concrete is :1:1.5:3. For 1m3 wet concrete, dry concrete required 52% more. That means for 1m3 wet concrete, dry concrete required

#### NORMS FOR RATE ANALYSIS OF ROAD AND BRIDGE

2019-6-4  Lime Concrete, cement concrete grade M-10 and below a) Labour Skilled day 1.00 Unskilled day 24.00 b) Equipment Tractor-trolley hour 6.00 B Cement Concrete Grade M-15 & M-20 Unit = cum, (for 20.0 cum) a) Labour Skilled day 1.00 Unskilled day 30.00 b) Equipment Tractor-trolley hour 6.00

#### Experimental Studies and Analysis of Strength Properties

2020-3-16  Experimental Studies and Analysis of Strength Properties of High Volumes of Slag Concrete for Rigid Pavements T. Vijaya Gowri, P. Sravana, P. Srinivasa Rao Abstract: Concrete is one of the most prevalent construction materials, in which cement is

#### how we calculate of Sand, cement and aggregate of M20

2016-2-16  M20 (1 cement :1.5 sand :3 stone/brick aggregate). To determine the proportions you have to perform mix design, for this you have to find out the sp.gr. of


text: The Misinterpretation of Climate Forecasts and their Economic Impacts to the Agricultural Sector | CLIMAS

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Optimality conditions (NLP)

This page describes necessary and sufficient conditions for local optimality in (continuous) nonlinear programming (NLP) optimization formulations.

When solving a continuous nonlinear minimization problem:

minimize $f(\mathbf{x})$

subject to $\mathbf{g}(\mathbf{x})\leq \mathbf{0}$

$\mathbf{h}(\mathbf{x}) = \mathbf{0}$
$\mathbf{x}\subseteq\Re^{n}$

a global minimum is a point such that no other feasible point has a lower objective function value. A local minimum is a point such that all feasible points in the neighborhood immediately surrounding the point have higher objective function values.

Because local optimality depends only on the small neighborhood surrounding the point, it is possible to derive necessary and sufficient conditions for local optimality using a Taylor series expansion. NLP algorithms in general search for points that satisfy these conditions. If the NLP formulation is convex, then there is only one local minimum, which is also the global minimum. If the formulation is nonconvex, these conditions do not guarantee global optimality.

Unconstrained NLP

For an unconstrained problem:

minimize $f(\mathbf{x})$

a candidate point $\mathbf{x}_\dagger$ can be tested for local optimality by writing the Taylor series expansion about the point:

$f = f(\mathbf{x}_\dagger) + \bigg(\frac{\partial f}{\partial \mathbf{x}}\bigg)_\dagger\partial \mathbf{x} + \frac{1}{2} \partial \mathbf{x}^{T} \bigg(\frac{\partial ^{2} f}{\partial \mathbf{x}^{2}}\bigg)_\dagger \partial \mathbf{x} + ...$

where $\partial \mathbf{x} = (\mathbf{x} - \mathbf{x}_\dagger)$

If $\mathbf{x}_\dagger$ is a local minimum, then, by definition, it must be true that all points in the immediate neighborhood have a higher objective function value - i.e.: there exists an ε > 0 such that

$f(\mathbf{x}_\dagger + \partial \mathbf{x}) - f(\mathbf{x}_\dagger) > 0$

$\forall \partial \mathbf{x}:||\partial \mathbf{x}|| < \epsilon$

Necessary condition

For small $\partial\mathbf{x}$ (i.e.: for the region in the immediate neighborhood of the candidate point), the first order term of the Taylor series dominates, and higher order terms are negligible. Since the first order term alone cannot satisfy the condition of a local minimum, the linear term must be zero as a necessary condition (so that higher order terms will determine the nature of the point):

$\bigg(\frac{\partial f}{\partial \mathbf{x}}\bigg)_\dagger = \mathbf{0}$

which is also written as

$\nabla_{\mathbf{x}}f = \mathbf{0}$

Any point satisfying this necessary condition is called a stationary point.

Sufficient condition

If the necessary condition is satisfied, the second order term of the Taylor series will dominate for small $\partial\mathbf{x}$. If the second order term is positive for all (small) $\partial\mathbf{x}$, this is sufficient to determine a minimum:

$\partial\mathbf{x}^{T}\bigg(\frac{\partial^{2}f}{\partial\mathbf{x}^{2}}\bigg)_\dagger \partial\mathbf{x}> \mathbf{0}; \forall \partial \mathbf{x}$

This condition is equivalent to saying that $\frac{\partial^{2}f}{\partial\mathbf{x}^{2}}$ is positive definite at the point $\mathbf{x}_\dagger$, which can be tested by checking that all eigenvalues of the Hessian matrix at the candidate point are positive.

Common Mistake: While it is common to mention only the second order term in discussing sufficiency conditions for optimality, the Taylor series derivation implies other possible sufficiency conditions: If the second order term is zero for any particular direction $\partial\mathbf{x}$, then higher order terms dominate along those directions, and their effects must be examined. A common mistake is to believe that a point with both first and second derivatives of zero is necessarily an inflection point. This is not necessarily the case: For example, consider the function f(x) = x4, which has a minimum at zero where the first three derivatives are zero and the fourth order term dominates, creating the sufficiency condition.

Constrained NLP

If the NLP optimization problem has constraints,

minimize $f(\mathbf{x})$

subject to $\mathbf{g}(\mathbf{x})\leq \mathbf{0}$

$\mathbf{h}(\mathbf{x}) = \mathbf{0}$

the problem can be reformulated in Lagrangian form to derive analogous optimality conditions. These conditions are again derived from a Taylor series expansion in the reduced space, although the derivation is not provided here:

Necessary condition

The Karush-Kuhn-Tucker (KKT) conditions are the first-order necessary conditions for constrained problems (optimality conditions for unconstrained problems are a special case). They can be stated as:

$\nabla L(\mathbf{x_*}) = \nabla f(\mathbf{x_*}) + \mathbf{\lambda}^T \nabla \mathbf{h(x_*)} + \mathbf{\mu}^T \nabla \mathbf{g(x_*)} = \mathbf{0}^T$
$\mathbf{h(x_*})=0$
$\mathbf{g(x_*)} \leq 0$

where $\mathbf{x_*}$ is the solution satisfied KKT condition, and $\mathbf{\lambda}^T \neq 0 \mbox{ , } \mathbf{\mu}^T g=0 \mbox{ , } \mathbf{\mu} \geq 0$

Sufficient condition

The second-order sufficient condition for local optimality in unconstrained models is:

$\partial \mathbf{x}^T \mathbf{H^*} \partial \mathbf{x} > 0$

where the Hessian matrix $\mathbf{H^*} = \nabla^2 L(\mathbf{x_*})$. To satisfy the sufficient condition, the Hessian matrix needs to be positive definite on the subspace tangent to the active constraints. Because a Hessian matrix is symmetric, it is positive definite when all eigenvalues are positive. A point that satisfies these necessary and sufficient conditions is a local minimum.


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Master's Dissertation
DOI
10.11606/D.14.2010.tde-27062013-093633
Document
Author
Full name
Eduardo Wilde Bárbaro
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2010
Supervisor
Committee
Oliveira, Amauri Pereira de (President)
Castro Filho, Belmiro Mendes de
Title in Portuguese
Investigação da camada limite planetária noturna na região metropolitana de São Paulo utilizando o modelo LES
Keywords in Portuguese
Modelo LES
Região Metropolitana de São Paulo
Abstract in Portuguese
Title in English
Investigation of the nocturnal boundary layer in the Metropolitan Region of São Paulo
Keywords in English
LES model
Metropolitan
Nocturnal Boundary layer
Abstract in English
The main objective of this work is to investigate the temporal and spatial evolutions of the planetary boundary layer (PBL) in the city of São Paulo during the nighttime period, using a large-eddy simulation (LES) model. It was simulated the 3-dimensional fields of the three components of the wind speed, potential temperature and carbon monoxide concentration. Three properties of nocturnal PBL were investigated: a) PBL depth; b) Low level jet (LLJ) and c) Turbulent dispersion of CO. The diurnal evolution of the turbulent fluxes of sensible heat and CO was also analyzed. Initially, a validation procedure was carried considering the performance of LES model in to simulate the behavior of the PBL for convective, neutral and stable conditions using as reference simulation results available in the literature. The validation was performed by comparing the mean vertical profiles of horizontal wind, potential temperature, variance of wind speed components and the turbulent kinetic energy (TKE) equation components. They indicated that the actual version of LES model is capable to simulate the entire cycle of the PBL diurnal evolution over a homogeneous and flat surface. Once validated, the LES model was applied to simulate the PBL for a complete diurnal cycle over a flat and homogeneous surface with aerodynamic roughness length representative of a typical urban area of São Paulo. Four simulations were designed to investigate the nighttime PBL evolution for winter conditions in São Paulo, using as input, monthly average hourly values of potential temperature and monoxide carbon observed at the surface during June in São Paulo. The mean condition for clear sky days observed in June in São Paulo was also considered as input in these simulations. The impact of wind intensity was also analyzed by considering as the external forcing in these simulations a constant background geostrophic wind of $5$ and $10 ms^{-1}$ from West. The dataset used in this work was observed in the micrometeorological platform of IAG (air temperature and sensible heat flux) and at the surface station of environmental agency of the state of São Paulo (CETESB) locate at Lapa (CO and wind speed). The results indicate that the height of stable PBL was simulated consistently with the boundary conditions and external forcing, indicating that during June the in São Paulo the PBL height may vary from 100m (mean condition) and 62m (clear days condition) at the beginning of the night to 275m (mean condition) and 203m (clear sky conditions) at the end of nighttime. It was verified that the turbulence in the Stable PBL is maintained by the mechanical production of TKE and dissipated, mainly, by the negative thermal production. Molecular dissipation has a secondary role and turbulent transport of TKE does not affect the stable PBL. All the empirical formulations used here reproduced the order of magnitude of the stable PBL height. The best performance was obtained by $h = 700 u_*$ and $h = 0.5 \sqrt{\frac{u_* L}{\left|fight|}}$. The simulated nocturnal LLJ indicated that for São Paulo the inertial oscillation yields a maximum intensity is $7.1 ms^{-1}$ at $210m$ and 05:30LT (forcing of $5 ms^{-1}$) and $14.5 ms^{-1}$ at $420m$ at 05:30LT (forcing of $10 ms^{-1}$). In both cases the LLJ intensified the turbulence at the top of the stable PBL. The simulated spatial and temporal evolution of the carbon monoxide concentration shows a pattern of turbulent dispersion consistent with the expected one for winter time in the city of São Paulo. Finally, LES model is able to reproduce the main features of the diurnal evolution of turbulent sensible heat and carbon monoxide fluxes at the surface for São Paulo during the winter.


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# Modifying appserver.home property in build.properties file NOT working

Melinda Savoy
Ranch Hand
Posts: 387
• 0
I am going through a spring tutorial and I'm trying to modify the appserver.home property with an absolute path value in the build.properties file so that it can find my tomcat server.

This is what I'm trying to change it to:

The original setting was appserver.home=\${user.home}/server/apache-tomcat-7.0.25

The \${user.home} value is defined as: C:\Users\Melinda and because my server is not installed in this directory then I get the following error when I try to refresh my build file:

springapp C:\Users\Melinda\workspace\SpringTutorial\springapp\"C:\server\apache-tomcat-7.0.25"\lib does not exist.

I'm sure I'm doing something stupid.

Any help/direction would be appreciated.

Thank you.

Melinda Savoy
Ranch Hand
Posts: 387
• 0
Sorry guys. I just found another post that resolved my issue. In the build.xml file the following classname is deprecated:

<classpath refid="catalina-ant-classpath"/>

The classname needed to be corrected to: "org.apache.catalina.ant.DeployTask"

Thanks anyway. Sorry for the post.

Jan Cumps
Bartender
Posts: 2575
11
• 0
Melinda Savoy wrote:Sorry guys. I just found another post that resolved my issue. In the build.xml file the following classname is deprecated:

<classpath refid="catalina-ant-classpath"/>

The classname needed to be corrected to: "org.apache.catalina.ant.DeployTask"

Thanks anyway. Sorry for the post.

That is two times the same: org.apache.catalina.ant.DeployTask ?

Melinda Savoy
Ranch Hand
Posts: 387
• 0
Sorry, Jan. The initial post should have stated:


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# An algebra problem by Tammu Triveni

Algebra Level pending

The variable $$A$$ varies inversely with $$B$$. $$A$$ is $$10$$ when $$B$$ is $$100$$.Find $$A$$ when $$B$$ is $$250$$?

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# zbMATH — the first resource for mathematics

Existence and asymptotic behavior of radially symmetric solutions to a semilinear hyperbolic system in odd space dimensions. (English) Zbl 1129.35045
The authors study the following semilinear hyperbolic systems in odd space dimensions: $\partial_t^2 u_1-c^2_1\Delta u_1=F(u_2),\qquad \partial_t^2 u_2-c^2_2\Delta u_2=G(u_1)$ for $$(x,t)\in {\mathbb R}^n\times {\mathbb R}$$ and for nonlinearities $$F$$ and $$G$$ of a polynomial growth. The main goal of the paper is to prove the existence of a small amplitude solution which is asymptotic to the free solution as $$t\to-\infty$$ in the energy norm, and to show it has a free profile as $$t\to +\infty$$. Here, the approach is based on the previous work of the authors [Hokkaido Math. J. 24, No. 2, 287–336 (1995; Zbl 0840.35063)], which consists in using a weighted $$L^2$$-norm to get suitable a priori estimates as well as in the restriction of the attention to radially symmetric solutions. The obtained results extend the previous three-dimensional theory published in [H. Kubo, K. Kubota, Adv. Differ. Equ. 7, No. 4, 441–468 (2002; Zbl 1223.35232)].

##### MSC:
 35L55 Higher-order hyperbolic systems 35L70 Second-order nonlinear hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs
Full Text:
##### References:
 [1] Agemi, R., Kurokawa, Y. and Takamura, H., Critical curve for p-q systems of nonlinear wave equations in three space dimensions, J. Differential Equations, 167, 2000, 87–133. · Zbl 0977.35077 · doi:10.1006/jdeq.2000.3766 [2] Asakura, F., Existence of a global solution to a semi-linear wave equation with slowly decreasing initial data in three space dimensions, Comm. Partial Differential Equations, 11, 1986, 1459–1487. · Zbl 0612.35089 · doi:10.1080/03605308608820470 [3] Del Santo, D., Global existence and blow-up for a hyperbolic system in three space dimensions, Rend. Istit. Mat. Univ. Trieste, 29, 1997, 115–140. · Zbl 0933.35122 [4] Del Santo, D., Georgiev, V. and Mitidieri, E., Global existence of the solutions and formation of singularities for a class of hyperbolic systems, Geometric Optics and Related Topics, F. Colombini and N. Lerner (eds.), Progress in Nonlinear Differential Equations and Their Applications, Vol. 32, Birkhäuser, Boston, 1997, 117–140. · Zbl 0893.35066 [5] Del Santo, D. and Mitidieri, E., Blow-up of solutions of a hyperbolic system: the critical case, Differ. Equ., 34(9), 1998, 1157–1163. · Zbl 1032.35126 [6] Deng, K., Nonexistence of global solutions of a nonlinear hyperbolic system, Trans. Amer. Math. Soc., 349, 1997, 1685–1696. · Zbl 0960.35063 · doi:10.1090/S0002-9947-97-01841-2 [7] Deng, K., Blow-up of solutions of some nonlinear hyperbolic systems, Rocky Mountain J. Math., 29, 1999, 807–820. · Zbl 0945.35054 · doi:10.1216/rmjm/1181071610 [8] Hidano, K., Nonlinear small data scattering for the wave equation in $$\mathbb{R}$$4+1, J. Math. Soc. Japan, 50, 1998, 253–292. · Zbl 0958.35085 · doi:10.2969/jmsj/05020253 [9] John, F., Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math., 28, 1979, 235–268. · Zbl 0406.35042 · doi:10.1007/BF01647974 [10] Kubo, H., On the critical decay and power for semilinear wave equations in odd space dimensions, Discrete Contin. Dyn. Syst., 2, 1996, 173–190. · Zbl 0948.35082 · doi:10.3934/dcds.1996.2.173 [11] Kubo, H. and Kubota, K., Asymptotic behaviors of radially symmetric solutions of = |u| p for super critical values p in odd space dimensions, Hokkaido Math. J., 24, 1995, 287–336. · Zbl 0840.35063 [12] Kubo, H. and Kubota, K., Asymptotic behaviors of radially symmetric solutions of = |u| p for super critical values p in even space dimensions, Japan. J. Math., 24, 1998, 191–256. · Zbl 0929.35013 [13] Kubo, H. and Kubota, K., Asymptotic behavior of classical solutions to a system of semilinier wave equations in low space dimensions, J. Math. Soc. Japan, 53, 2001, 875–912. · Zbl 1016.35050 · doi:10.2969/jmsj/05340875 [14] Kubo, H. and Kubota, K., Scattering for systems of semilinier wave equations with different speeds of propagation, Adv. Differential Equ., 7, 2002, 441–468. · Zbl 1223.35232 [15] Kubo, H. and Ohta, M., Critical blowup for systems of semilinear wave equations in low space dimensions, J. Math. Anal. Appl., 240, 1999, 340–360. · Zbl 0945.35016 · doi:10.1006/jmaa.1999.6585 [16] Kubo, H. and Ohta, M., Small data blowup for systems of semilinear wave equations with different propagation speeds in three space dimensions, J. Differential Equations, 163, 2000, 457–492. · Zbl 0964.35093 · doi:10.1006/jdeq.1999.3740 [17] Kubota, K. and Mochizuki, K., On small data scattering for 2-dimensional semilinear wave equations, Hokkaido Math. J., 22, 1993, 79–97. · Zbl 0768.35063 [18] Pecher, H., Scattering for semilinear wave equations with small data in three space dimensions, Math. Z., 198, 1988, 277–289. · Zbl 0627.35064 · doi:10.1007/BF01163296 [19] Tsutaya, K., Scattering theory for semilinear wave equations with small data in two space dimensions, Trans. A. M. S., 342, 1994, 595–618. · Zbl 0812.35091 · doi:10.2307/2154643
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.