Study On The Blasting And Extinction Of The Solution Of Parabolic Equations

In this paper, we study the blow-up behavior of parabolic problem and the ex-tinction solution for the p-Laplace parabolic equation systems.In chapter 1, we discuss the blow-up behavior of the nonnegative of solution to a singular and degenerate nonlocal parabolic equation with nonlocal nonlinear boundary condition where Ω is a bounded domain in RN(N ≥ 1) with a smooth boundary Ω, 0 <a < 1, p and q are positive parameters. Under certain conditions, the existence and nonexistence of the global solution will be given. Furthermore, we get the global blow-up behavior, blow-up set of the blow-up solution and the blow-up estimates are also obtained.In chapter 2, we investigate the extinction solutions for the p-Laplace parabolic equation systems with Dirichlet boundary conditions for the following forms:where 1 < p, q < 2, α,β > 0.