渗流方程差分解的收敛性

渗流方程是拟线性退化抛物型方程。1—4]讨论了弱解的存在唯一性问题。由于非线性扩散系数有零点,其解可以不光滑。在5,6]中研究了渗流方程 u_t=(u~m)_(xx),m>1的差分方法问题,对光滑区和弱间断点给以分别处理。渗流方程的解是连续的,但在有些点上导数不存在。因此,不能用Taylor展开估计截断误差的方法证明差分解的收敛性。

CONVERGENCE OF DIFFERENCE SOLUTIONS FOR FILTRATION EQUATIONS

The porous media equations are degenerate parabolic, their solutions may be weak-ly discontinuous. In this paper we study the stability and convergence of implicit dif-ference solutions for the second boundary problems of filtration equations u_t=f(u)_(xx),The diffusion coefficients f'(u) may be degenerate or contain singular points. Hencethe existence of solutions for filtration equations is also obtained.