Abstract
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.
Highlights
For some animal species, different groups may live in different habitats separated by free boundaries
We consider the one-dimensional ecological models with N -species where the mankind?s influence is taken into account
To describe the free boundary problem, we introduce some notations: QT := (, d) ×
Summary
Different groups may live in different habitats separated by free boundaries (see [ ]). By the approximation and estimate methods, we show the existence and uniqueness of the solutions for diffraction problem ). Section is concerned with the local existence of solutions for the free boundary problem
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