On nonclassical problems for first-order evolution equations

被引：6

作者：

Avalishvili, Gia ^{[1
]}

Avalishvili, Mariam ^{[2
]}

机构：

[1] I Javakhishvili Tbilisi State Univ, Fac Exact & Nat Sci, GE-0179 Tbilisi, Georgia

[2] Univ Georgia, Sch Math & Informat Technol, GE-0175 Tbilisi, Georgia

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2011年 / 18卷 / 03期

关键词：

Abstract first-order evolution equations; parabolic equations and systems; nonlocal initial conditions; variational methods; NONLOCAL BOUNDARY;

D O I：

10.1515/GMJ.2011.0028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The present paper deals with nonclassical initial-boundary value problems for parabolic equations and systems and their generalizations in abstract spaces. Nonclassical problems with nonlocal initial conditions for an abstract first-order evolution equation with time-dependent operator are considered, the existence and uniqueness results are proved and the algorithm of approximation of nonlocal problems by a sequence of classical problems is constructed. Applications of the obtained general results to initial-boundary value problems for parabolic equations and systems are considered.

引用

页码：441 / 463

页数：23

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