On Solvability of Parabolic Equations with Essentially Nonlinear Differential-Difference Operators

被引：0
|
作者：
O. V. Solonukha
机构：
[1] Federal Research Center Computer Science and Control of the Russian Academy of Sciences,
来源：
Siberian Mathematical Journal | 2023年 / 64卷
关键词：
nonlinear parabolic functional-differential equation; shift operator in the space variables; operator with semibounded variation; 517.9;
D O I：
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中图分类号：
学科分类号：
摘要：
We consider the first mixed boundary value problem for a nonlinear differential-difference parabolic equation. We give some sufficient conditions for the nonlinear differential-difference operator to be radially continuous and coercive as well as has the property of (V,W)-semibounded variation (in this case we provide the algebraic condition of strong ellipticity for an essentially nonlinear differential-difference operator). We also justify the existence theorems for a generalized solution.
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页码：1237 / 1254
页数：17
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