Numerical Methods For Computing Nonlinear Eigenpairs Of The P-Laplace Operator

For the scientific research and engineering at the present stage in the calculation of the solution of partial differential equations, eigenpair problem is very important, eigen-pair finite element method approach to the problem of the idea can be traced back to hundreds of years ago, the problem of the vibration of elastic Rayleigh Describe the ba-sic frequency of Rayleigh-quotient minima. Society to modern, in the elastic vibration, nuclear reactor multigroup diffusion, cylindrical and shell buckling, electronic struc-ture, fluid mechanics, electromagnetic field A lot of applications, features constantly need to solve the problem of the differential equation. While p-Laplace equation in non-Darcian and glaciology, turbulence theory, climatology, nonlinear diffusion, flow in porous media with power-law fluid mechanics and material science, mathematical modeling has important applications.This paper mainly research on nonlinear eigenpair problem of p-Laplace equation with iso-homogeneous and eigenpair problem of a class of non cooperative p-Laplace equations. Firstly, based on the variational principle, and the descent direction method, successfully solving a class of iso-homogeneous p-Laplace equations of the multi group characteristics on; then, in the local minimax orthogonal method (LMMOM) on the basis of the calculation method is put forward on the problem, a solution of p-Laplace equations feature. Through a large number of numerical tests on a square region and the circular region, verify the effectiveness of the improved calculation method and the feasibility of.