ON THE GLOBAL EXISTENCE OF SOLUTIONS TO QUASILINEAR PARABOLIC EQUATIONS This work was partially supported by the National Natural Science Foundation of China, the Natural Science Foundation of Guangdong Province, and the Foundation of Zhongshan University Advanced Research Center.

Abstract

We prove, under quite general assumptions, the global existence of classical solutions for quasilinear parabolic equations in bounded domains with homogeneous Dirichlet boundary conditions. The same results for weakly coupled reaction-diffusion systems are also given.