The Blow-up Problems Of Several Reaction-diffusion Equations

This paper mainly studies the blow-up phenomenon of several class of reaction-diffusion equations,which are introduced in four chapters as following:Chapter 1 is introduction,we introduce the research status and background of reaction-diffusion equations.Chapter 2,we study the initial boundary value problems of p-Laplacian reaction-diffusion equations(?) under some appropriate conditions,we prove the global existence of the solutions.By using Sobolev inequalities,we prove the solutions blow up in finite time.In addition,the estimation of upper and lower bounds for blow-up time are given.Chapter 3,we deal with initial boundary value problems for a class of nonlinear divergence type reaction-diffusion equations (?)where a(x)is weighted function.we give the estimates of upper and lower bounds of blow up time.Chapter 4,we focus on the initial boundary value problems for a class of reaction-diffusion equations (?)where k(t)=1/|?|(??f(u)dx).Under some appropriate assumptions,we prove the solution blows up in finite time.