Research On The Blow-up, Quenching And Global Existence Of The Solutions Of Two Types Of Nonlinear Parabolic Equations

In this work,we consider the global existence,blow-up and extinction behavior of solutions of two kinds of nonlinear parabolic partial differential equations.In chapter 1,we consider the blow-up and extinction behavior of solutions to a class of p-biharmonic parabolic equation where D is Ω ×（0,t*）,S in（?）Ω×（0,+∞）,Ω（?）R^N（N≥1）上 is a bounded domain with smooth boundary（?）Ω,f:[0,∞)→[0,∞)is a locally Lipschitz function,m（Ω）represents the Lebesgue measure of the domain Ω,γ ≥ 0,max[1,2N/N+4]<p ≤2,u₀（x）∈ L^∞（Ω）\∩W^2,p（Q）.In chapter 2,we consider the global existence and non-extinction properties of solutions to a nonlocal parabolic equation where Ω is a bounded domain of R^N（N ≥ 2）with smooth boundary（?）Ω.