Asymptotic Estimates And Fujita Exponents In Parabolic Systems With Variable Coefficients

In the present paper,we study a class of nonlinear parabolic partial differential equations with time-weighted coefficients,we are going to study the impact of nonlinear reaction on the critical Fujita exponents.Moreover,the exponents classification of the simultaneous and non-simultaneous blow-up are determined.Finally,the upper and lower bounds estimates of blow-up rates and blow-up times of blow-up solution are obtained.This article is divided into six chapters:The first and second chapters of the article firstly introduce the background,significance and current research status of the present study,then give the questions and necessary knowledge reserve.In the third chapter,we determine the critical Fujita exponents of solutions prescribed by the traditional component of solutions exponents,the coefficients of weighted functions and the first eigenvalue of Laplacian operator with zero Dirichlet boundary.In chapter 4,we distinguish completely simultaneous blow-up from non-simultaneous blow-up of two components of solutions.It is interesting that different initial data could lead to different blow-up rates even in the same region.In chapter fifth and sixth,the upper and lower bounds estimates of blow-up rates and blow-up times of blow-up solution are studied according to different blow-up phenomenon and singularity phenomenon.