一类反应扩散方程的边界元分析

引入一类不同方向具有不同扩散系统的反应扩散方程的边界元方法，利用Ｆｏｕｒｉｅｒ积分变换导出方程的基本解，从而得到该方程初边值问题的边界积分方程和边界变分方程及其解的存在惟一性定理，证明了边界元方法的收敛性，从理论上完善了抛物型方程边值问题的边界元方法。

Boundary Element Analysis for a Class of Two Dimension Reaction Diffusion Equation

The initial boundary value problem for a class of two dimension reaction diffusion equation with different diffusion coefficients in different orientations is dealt with by means of boundary element method. We try to present a boundary integral equation, its variational formulation and the existence uniqueness of the solution to the problem by using the fundamental solution derived from Fourier integral transformation. The convergence results of the approximation solution are given, and so the boundary element method of initial boundary value problem for parabolic equation is theoretically improved.