Abstract

We reduce solution of the Cauchy problem for forward and backward systems of nonlinear parabolic equations to solution of certain stochastic problem formulated in terms of stochastic differential equations. Then we state existence and uniqueness theorems for solutions of the resulting stochastic systems and deduce existence and uniqueness of the Cauchy problem solutions for the original parabolic systems. As a by-product we derive stochastic representations of solutions to the Cauchy problem for some classes of nonlinear parabolic equation systems.

中文翻译：

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非线性抛物型方程组Cauchy问题解的概率解释。

摘要

我们将非线性抛物方程组的正向和反向系统的柯西问题的解简化为以随机微分方程表示的某些随机问题的解。然后，我们给出了所得随机系统解的存在性和唯一性定理，并推论了原始抛物型系统的柯西问题解的存在性和唯一性。作为副产品，我们获得了某些类别的非线性抛物方程组对Cauchy问题解的随机表示。