Abstract

The first mixed boundary value problem for a nonlinear functional-differential equation of parabolic type with shifts in the spatial variables is considered. Sufficient conditions are proved under which a nonlinear differential-difference operator is demicontinuous, coercive, and pseudomonotone on the domain of the operator \(\partial_t\). Based on these properties, existence theorems for a generalized solution are proved.

中文翻译：

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具有空间变量平移的非线性抛物型泛函微分方程的可解性

摘要

考虑具有空间变量偏移的抛物型非线性函数微分方程的第一个混合边值问题。证明了非线性微分-差分算子在算子\(\partial_t\)域上半连续、强制且伪单调的充分条件。基于这些性质，证明了广义解的存在定理。