关键词: 挠射问题, 椭圆方程组, 边界相交的交界面, 逼近方法

Abstract:

The paper deals with  the n-dimensional diffraction problem for quasilinear elliptic system on a bounded domain, where the coefficients of the equations are allowed to be discontinuous on the interfaces and the interfaces   are allowed to
intersect with the outer boundary of the domain. By constructing an approximation diffraction problems with interfaces
which do not intersect with the outer boundary, using  various estimates and approximation method, and investigating the regularity of the weak solutions, we get the existence of solutions of the problem. An application is given to the Lotka-Volterra cooperation model with two cooperating species.

Key words: Diffraction problem,  Elliptic systems,  Boundary intersecting interfaces, Approximation method