Quenching And Blow-up Of The Solutions For Two Classes Of Nonlinear Evolution Equations

The study on the properties of the solutions for the nonlinear evolution equations isone of the important branches of partial differential equation. In Chapter2, we deal witha nonlinear p-Laplacian equation with singular boundary conditions. Under properconditions, the solution of this equation quenches in finite time and the only quenchingpoint that is x1are obtained. Moreover, the quenching rate of this equation isestablished. Finally, we give an example of an application of our results. In Chapter3,we consider the global nonexistence of solutions for nonlinear p （x）-Kirchhoff systemswith dynamic boundary conditions, which involve nonlinear external dampingterms Q=Q（t,x,u,ut）, nonlinear driving forces f=f（t,x,u）and may be affected by aperturbation of the type|u|^{p （x）-2}u. We provide some concrete examples offunctions f and Q, and give useful applications to the main theorem in particularsubcases.