The Global Existence And Blow-up Of Two Kinds Of Nonlinear Parabolic Equations

In this paper we mainly utilize super and sub solution techniques, use comparision principle and construct appropriate supersolution and subsolution by eigenfunctions to discuss two kinds of nonlocal nolinear parabolic systems with homogeneous Dirichlet boundary condition.In this paper, Chapter 2 discusses a nonlocal nonlinear parabolic equation: by constructing appropriate supersolutions and subsolutions, we get the blow-up and global existence of the equations.If m＞P₁, n＞P₂, and q₁q₂＜(m-p₁)(n-P₂), every nonnegative solution of the equations is global.If m＜p₁orn＜p₂orq₁q₂＞(m -p₁)(n-P₂), then the nonnegative solution blows up in finite time for sufficiently large initial values and exists globally for sufficiently small initial values.If m＞p₁, n＞P₂, and q₁q₂=(m-p₁)(n-P₂), every nonnegative solution of the equations is global provided that the magnitude of the domain (|Ω|) is sufficiently small. Chapter 3 is dedicated to studying a parabolic system with localized nonlinear reactions: We get the blow-up estimates of solutions to the equations.For the Cauchy problem, we get the blow-up condition and blow-up rate; for the first initial boundary problem, besides establishing the blow-up rates, we obtain the size of the boundary layer.