Upper And Lower Bounds Of Blow-up Time For Two Classes Of Nonlinear Parabolic Equations With Nonlocal Boundary Conditions

In this dissertation,we mainly studies the blow-up problem of two types of nonlinear parabolic equation(systems)under non-local boundary conditions.By constructing appropriate auxiliary functions,using improved differential inequality techniques,combined with Sobolev space theory and the elementary solution of differential equations in ordinary differential equations.Under non-local boundary conditions,we discussed the sufficient conditions for the blow-up of the quasi-linear parabolic equations and nonlinear reactions diffusion equations.In addition,When blow up occurs,the upper and lower bounds of blow up time for these two kinds of equations are obtained.The full text is divided into four chapters.In Chapter 1,describes the research background and significance of the blowing up problem of nonlinear parabolic equations(systems),as well as the research status and frontier trends of domestic and foreign experts and scholars specializing in partial differential equations in recent years.Finally,the main work of the full text is introduced,and the prerequisite knowledge for writing is given.In Chapter 2,We study a class of quasilinear parabolic equations with blow up solutions,and the blow-up of the solution is studied.by making appropriate assumptions on the function,establishing appropriate auxiliary functions,using Sobolev inequality and improved differential inequality techniques,combined with the elementary solution of first-order ordinary differential equations,the sufficient condition of blow-up is obtained and the upper bound of the blow-up time is estimated;The lower bounds of blow-up time are estimated when blow-up occurs.In Chapter 3,the blow up problem for a class of Quasilinear Parabolic Equations with non-local boundary is studied.Appropriate auxiliary functions are constructed,and improved differential inequality techniques such as Sobolev inequality,H(?)lder inequality,Young inequality,and basic inequalities are used.The sufficient conditions are given to ensure the solution blow-up in a finite time,the upper and lower bounds of blow-up time are estimated when blow-up occurs.In Chapter 4,the main conclusions are summarized.What's more,we put forward the prospects for further study of nonlinear parabolic equations(systems).