BLOW-UP PROBLEMS FOR A CLASS OF QUASILINEAR PARABOLIC EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS
In this paper, the blow up of smooth local solutions and weak local solutions for a class of quasilinear parabolic equations u , t= V(a(w)Vu) + f(x,u,q,t) {q= |Vup) subject to Neumann boundary conditions are studied. By constructing an auxiliary function and using H o p f s maximum principles and convex function method, some nonexistence theorems of global solutions and the Upper bounds of "blow-up time" as well as the upper estimate of the blow-up rate of nonglobal solutions are obtained under some suitable assumptions on a, f and initial date.