The Upper And Lower Bound Estimates On The Blow-up Time Of The Solutions For Two Classes Of Nonlinear Parabolic Equation(System)

In this dissertation,the solutions of two kinds of nonlinear parabolic equation(system)are studied.Under different boundary value conditions,we discuss the profiles of solutions to parabolic equation(system)with different source terms,which include the global existence,sufficient conditions for the blow-up,and the upper and lower bounds of blow-up time are estimated when blow-up occurs.In the first chapter,we mainly introduce research background of the problem,as well as research progress and achievements of the reaction diffusion equation and the parabolic equation by domestic and foreign scholars in recent years.At the same time,the purpose and significance of this research are also introduced.Finally,we also introduce the main work of this paper.In the second chapter,we investigate an initial-boundary value problem for a quasilinear reaction-diffusion equation with weighted nonlocal inner absorption and nonlinear Neumann boundary condition.By constructing appropriate auxiliary functions and using the improved differential inequality techniques,we first obtained sufficient conditions for the existence of the global solution,and then the blow-up in finite time is studied and the upper and lower bounds of the blow-up time are obtained.In the third chapter,we deal with the blow-up phenomena for a system of reaction-diffusion equations with nonlinear boundary conditions.By using differential inequality technique and Sobolev inequality,the upper and lower bounds of blow-up time are estimated when blow-up occurs.In the fourth chapter,we sum up the problems and the conclusions of this dissertation,combing with the research results to make futher research prospects.