126071351
On the Uniqueness and Asymptotic Behaviour of Plasma Corners
118988523
BV Solutions to Evolution Problems with Time-Dependent Domains
In a Hilbert space H we consider evolution problems -du(t) ε A(t)u(t) on some interval [0, T], where every A(t): D(A(t))→ 2 H is a maximal monotone operator, and the correspondence t↦ A(t) is – in a suitable sense – of bounded variation or absolutely continuous.
18597173
ON THE DISCRETIZATION OF DEGENERATE SWEEPING PROCESSES
We prove existence theorems for evolution equations of the form −u(t) ∈ ∂δC(t)(Au(t)) with some maximal monotone and strongly monotone operator A : D(A)→ 2 . 1 – Introduction and main results We study the evolution problem (1) −u(t) ∈ ∂δC(t)(Au(t)) a.e. in [0, T ], u(0) = u0 ∈ D(A) , where A is a maximal monotone and strongly monotone operator in the real Hilbert space H, and t 7→ C(t) is a Hausdorff-continuous multifunction with closed convex values. Equations of this form arise from problems of the type −x(t) ∈ ∂δC(g(t, x(t))), which play an important rôle in elasticity theory, cf. [8, 3, 4] for more information. To solve (1) means that we have to find u ∈W 1,1([0, T ];H) and v ∈ L2([0, T ];H) such that u(0) = u0, u(t)∈D(A) a.e., v(t)∈Au(t)∩C(t) a.e. and −u′(t)∈∂δC(t)(v(t)) a.e. in [0, T ] . Our general assumptions are (H1) A:D(A)→2H\{∅} is a maximal monotone operator (abbreviated mmop) such that A = ∂ψ for some lsc, convex and proper ψ : H → R ∪ {∞}, and there exists a β > 0 such that (2) 〈Ax−Ay, x− y〉 ≥ β |x− y| for x, y ∈ D(A) . Received : December 31, 1996; Revised : April 4, 1997. Mathematical Subject Classification (1991): 34A60, 35K22.
121396560
Periodic Solutions of Conservative Non‐Smooth Dynamical Systems
We consider conservative non-smooth dynamical systems of the type ẍ+e+a sgn(x) = p(t) with an w-periodic forcing p, and we first prove the existence of periodic solutions in the non-resonant case for the corresponding differential inclusion. Moreover, in the resonant case w = 2π, we gave necessary and sufficient conditions on a and the first Fourier coefficient of p for periodic solutions to exist.
122068311
Yosida–Moreau Regularization of Sweeping Processes with Unbounded Variation
Lett↦C(t) be a Hausdorff-continuous multifunction with closed convex values in a Hilbert spaceHsuch thatC(t) has nonempty interior for allt. We show that the Yosida–Moreau regularizations of the sweeping process with moving setC(t), i.e., the solutions of[formula]are strongly pointwisely convergent asλ→0+to the solution of the corresponding sweeping process, formally written as[formula]
120017422
Unbounded Solutions in Non-Smooth Dynamical Systems at Resonance
We consider periodically forced non-smooth dynamical systems at resonance, described by differential inclusions, and we show that analogously to the case of ODEs all solutions are unbounded in the (x)-phase plane, if the first Fourier coefficient of the forcing is large compared to a certain quantity related to the nonlinearity.
189767414
Zappa products
121961938
Bilateral semidirect products of transformation semigroups