Solvability and maximal regularity of parabolic evolution equations with coefficients continuous in time

被引：72

作者：

Prüss, J ^{[1
]}

Schnaubelt, R ^{[1
]}

机构：

[1] Univ Halle Wittenberg, FB Math & Informatik, D-60120 Halle, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2001年 / 256卷 / 02期

关键词：

nonautonomous Cauchy problem; parabolic; maximal regularity; evolution family; evolution semigroup; Miyadera perturbation;

D O I：

10.1006/jmaa.2000.7247

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish maximal regularity of type LP for a parabolic evolution equation u'(t) = A(t)u(t) + f(t) with A(.) is an element of C([0, T], L(D(A(0)), X)) and construct the corresponding evolution family on the underlying Banach space X. Our proofs are based on the operator sum method and the use of evolution semigroups. The results are applied to parabolic partial differential equations with continuous coefficients. (C) 2001 Academic Press.

引用

页码：405 / 430

页数：26

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