A free boundary problem arising in the ecological models with N -species

Boundary value problems

Qi-Jian Tan¹ 

[1] Department of Mathematics, Chengdu Normal University, Chengdu, P.R. China

关键词: free boundary;    diffraction problem;    reaction-diffusion system;    existence;    fixed point theorem;    approximation method;    35R35;    35R05;    35K57;    35K20;   

DOI  :  10.1186/s13661-014-0267-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper is concerned with the one-dimensional free boundary problem for quasilinear reaction-diffusion systems arising in the ecological models with N-species, where some of the species are made up of two separated groups and the mankind’s influence is taken into account. In the problem under consideration, there are n free boundaries, the coefficients of the equations are allowed to be discontinuous on the free boundaries and the reaction functions are mixed quasimonotone. The aim is to show the local existence of the solutions for the free boundary problem by the fixed point method, and the global existence and uniqueness of the solutions for the corresponding diffraction problem by the approximation and estimate methods.

【 授权许可】

CC BY