Abstract

We consider the first boundary value problem for quasilinear parabolic differential–difference equations. The uniqueness and existence of generalized solutions are proved. The proofs are based on the theory of linear differential–difference equations and the theory of monotone (pseudomonotone) operators.

中文翻译：

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拟线性抛物线微分方程的第一边值问题

摘要

我们考虑拟线性抛物线微分差分方程的第一个边值问题。证明了广义解的唯一性和存在性。证明基于线性微分差分方程理论和单调（伪单调）算子理论。