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

共 50 条

[21] Regularity for parabolic equations with singular or degenerate coefficients
Hongjie Dong
Tuoc Phan
Calculus of Variations and Partial Differential Equations, 2021, 60
[22] COMBINING MAXIMAL REGULARITY AND ENERGY ESTIMATES FOR TIME DISCRETIZATIONS OF QUASILINEAR PARABOLIC EQUATIONS
Akrivis, Georgios
Li, Buyang
Lubich, Christian
MATHEMATICS OF COMPUTATION, 2017, 86 (306) : 1527 - 1552
[23] Maximal regularity for nonautonomous evolution equations
Amann, H
ADVANCED NONLINEAR STUDIES, 2004, 4 (04) : 417 - 430
[24] On the Maximal Regularity Property for Evolution Equations
Pyatkov, S. G.
AZERBAIJAN JOURNAL OF MATHEMATICS, 2019, 9 (01): : 137 - 155
[25] Maximal regularity of parabolic equations associated with a discrete Laplacian
Bui, The Anh
JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 375 : 277 - 303
[26] Runge–Kutta Time Discretization of Nonlinear Parabolic Equations Studied via Discrete Maximal Parabolic Regularity
Peer C. Kunstmann
Buyang Li
Christian Lubich
Foundations of Computational Mathematics, 2018, 18 : 1109 - 1130
[27] Maximal time regularity for degenerate evolution integro-differential equations
Favaron, Alberto
Favini, Angelo
JOURNAL OF EVOLUTION EQUATIONS, 2010, 10 (02) : 377 - 412
[28] Maximal time regularity for degenerate evolution integro-differential equations
Alberto Favaron
Angelo Favini
Journal of Evolution Equations, 2010, 10 : 377 - 412
[29] ELLIPTIC REGULARITY AND SOLVABILITY FOR PARTIAL DIFFERENTIAL EQUATIONS WITH COLOMBEAU COEFFICIENTS
Hoemann, Gunther
Oberguggenberger, Michael
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2004,
[30] Maximal Lp regularity for elliptic equations with unbounded coefficients
Da Prato, G
Vespri, V
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 49 (06) : 747 - 755

← 1 2 3 4 5 →