By using the first eigenvalue,the corresponding eigen function of the Laplacian operator and their properties,one quenching criterion of the solution and an estimate of the quenching time of the solution simultaneously are obtained.

Extinction of Solution for a Class of Ginzbur—Landau Models Reaction-Diffusion Equation in Population Problems;

Extinction and Positivity for p-Laplacian Parabolic Equation and Global Existence for p-Laplacian Parabolic System;

Extinction of Solutions for A Class of Reaction-Diffusion Equations

Study on Propagating Mechanism and Quenching of Premixed Flames in Narrow Channels;

quenching and the dead core problem,the blow-up results are derived for the fuel ignition models with agradient term,and which is similar to the models without the gradient term.

The propagation and quenching of unsteady premixed flames in narrow channels with cold walls are numerically investigated.

up anddie out Within a finite time by using the eigen─function method.

This paper considers the boundc ry value problems witll three type;of theboundary condit ions for nonl incar pseudo-hypcrbolic squat ions of generalized nerveconduction type, using thg cigenfunction mothod, the conditions for which the solutions blow up and die out in the finite time arc got.

It discusses how to blow up and die out of their solutions.

Global existence and quenching phenomena for a parabolic equation of the mean curvature type with nonlinear convection term;

Deriving the quenching phenomena to an initial-boundary value problem in a bounded domain in the R~n for the mean curvature equation with a nonlinear convection term:u_t-div｛σ(|u|~2)u｝+b(u)·u=0.

This dissertation is devoted to the global existence and quenching phenomena of the solution to a nonlinear parabolic equation of the mean curvature type and the blow-up conditions to another nonlinear parabolic equation.