Global Existence And Blow-up Phenomena Of One Classes Of Nonlinear Parabolic Equations

This paper research a class of nonlinear parabolic equations with nonlinear NEUMANN boundary conditions.In this paper,we mainly use the maximum principle,the differential inequality technique and energy model estimate and the theory of the correlation differential equation to study the whole existence of the solution of the nonlinear parabolic equation,and the lower bounds of the blow-up time when the blow-up occurs.The first chapter,we mainly introduce the research background of this paper,and the research progress of the parabolic equation and the achievements made by scholars at home and abroad in recent years.At the same time,it also expounds the main purpose and significance of this research.Finally,we also introduce the main work of this paper.The second chapter,we study a class of nonlinear parabolic equations with nonlinear NEUMANN boundary conditions.First we obtain the modulus of the gradient of the solution is bounded by the maximum principle,then we obtain the global existence of solution of the equation by using auxiliary function to establish the appropriate differential inequalities.In the third chapter,we introduce the initial boundary value problem for nonlinear parabolic equation with nonlinear NEUMANN boundary conditions.For the Nonlinear parabolic equation model in the second chapter,we study the lower bounds of the blow-up time when the solution of the equation is blow-up occurs by using the differential inequality technique and combining the theoretical knowledge of the relevant differential equations according to the appropriate assumptions.In the fourth chapter,we mainly summarize the problems and conclusions obtained in this paper,and the combination of these conclusions to make further study of nonlinear parabolic equations.