Global Weak Solutions For The Cauchy Problems Of A Class Of Reaction-Diffusion Equations

In this paper, we consider the Cauchy problems of a class of reaction-diffusion equations:This thesis mainly consists of three parts:First, this paper introduces the potential well. By using the potential well method, a family of potential wells are given.Then, Cauchy problem is studied by means of the family of potential wells. And the known results are generalized and improved essentially. We obtain a threshold result of global existence.Last, we discuss the case that the initial condition is changed And we have the blow up phenomenon of solutions for a given boundary condition. Last we study the asymptotic behavior of solutions.