具有奇性的P-Laplacian发展方程

The Evolutional P-Laplacian Equation with Singularity

在n-维单位球上研究具有奇性的P-Laplacian发展方程的定解问题,其奇异性出现在球心上。整体径向解的存在性依赖于参数p,q,τ的取值范围.文章利用紧映射原理求出p,g,τ适当的范围关系,主要问题的整体径向解存在.通过构造能量函数利用Galerkin’s方法、先验估计和弱解的极大值原理加以证明.

We consider the solvability of the initial-boundary value problem in a unit nball for the evolutional p-Laplacian equation with singular coefficients. The singularity is at the origin x ： 0. The existence of global radial solution depends on some conditions of the parameters p,q, τ .In this paper we solve the proper conditions of parameters using the compact mapping. Under the conditions, the main problem has global radial solution. We prove it by constracting the energy functions, by the use of Galerkin＇s method and pre-estimate and the maximum principle for the weak solution.