拟线性抛物型方程边值问题差分方程解的存在与惟一

Existence and uniqueness of solution to nonlinear difference equation for quasilinear parabolic boundary value problems

数值求解拟线性抛物型偏微分方程边值问题通常可归结为解非线性方程组,非线性方程组解的存在与惟一性是解方程组的前提.为此,用差分方法建立了数值求解一类拟线性抛物型方程边值问题的非线性方程,根据同胚理论得到了该方程组解存在与惟一的结果,并通过具体例子给予了说明.

A nonlinear equation for the boundary value problem of the quasilinear parabolic equation is set up by use of the difference method. The existence and uniqueness of the solution to the equation are verified based on the homeomorphism theory, and an example is given to show the rationality of the solution.