Existence and uniqueness of bounded weak solutions for some nonlinear parabolic problems

摘要

In this paper we study a class of nonlinear parabolic problems with p ( x , t ) $p(x,t)$ growth conditions. We prove the existence and uniqueness of bounded solutions to such a problem, with less constraint to p ( x , t ) $p(x,t)$ . Our results are generalizations of the corresponding results in the constant exponent case.