Solvability of initial boundary value problems for non-autonomous evolution equations

被引：1

作者：

Pyatkov, S. G. ^{[1
,2
]}

机构：

[1] Yugra State Univ, Chekhov St 16, Khanty Mansiisk 628012, Russia

[2] South Ural State Univ, Chelyabinsk, Russia

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2020年 / 20卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Operator-differential equation; Cauchy problem; Non-autonomous evolution equation; Maximal regularity; Initial boundary value problem; MAXIMAL REGULARITY; PSEUDODIFFERENTIAL-OPERATORS; INTERPOLATION; SPACES;

D O I：

10.1007/s00028-019-00516-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The initial boundary value problems for linear non-autonomous first-order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change with t. We study existence, uniqueness and maximal regularity of solutions in Sobolev spaces. In contrast to the previous results, we use only the continuity assumption on the operators in the main part of the equation.

引用

页码：39 / 58

页数：20

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