具边界相交交界面的拟线性椭圆方程组的挠射问题

Diffraction Problems for Quasilinear Elliptic Systems with Boundary Intersecting Interfaces

研究有界区域上的n维拟线性椭圆方程组的挠射问题,其中方程的系数在交界面上允许间断,而且交界面允许与区域外边界相交.通过构造一个交界面与外边界不相交的近似挠射问题,利用估计和逼近方法,并讨论弱解的正则性,得到了问题解的存在性,并将这些结果应用到两种群Lotka-Volterra互惠模型.

The paper deals with the n-dimensional diffraction problem for quasilinear elliptic system oil a bounded domain, where the coefficients of the equations are allowed to be discon- tinuous oil 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.