带梯度项的p-Laplacian方程正解的Blow-up

Blow-up of Positive Solutions for a Family of p-Laplacian Equations with a Gradient Term

研究了RN中一般区域上的一族带非线性梯度项的p-Laplacian方程解的Blow-up性质.通过构造适当的辅助函数,利用特征函数法和不等式技巧,给出了其齐次Dirichlet边值问题的正解产生Blow-up的充分条件,该方法也适用于研究其他带非线性源的退缩非线性抛物方程解的Blow-up问题.

The blow-up behavior of positive solutions for a family of p-Laplacian equations with nonlinear gradient term in general domain in RN is studied.By constructing an auxiliary function and using the eigenfunction method and inequality technic on it,the sufficient conditions for blow-up positive solutions of the equations with homogeneous Dirichlet boundary conditions are obtained.The methods in here could be applied to a wide class of nonlinear degenerate parabolic equations with nonlinear sources.