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Semilinear parabolic equations involving measures and low regularity data


Amann, H; Quittner, P (2004). Semilinear parabolic equations involving measures and low regularity data. Transactions of the American Mathematical Society, 356(3):1045-1119 (electronic).

Abstract

A detailed study of abstract semilinear evolution equations of the form u + Au = µ(u) is undertaken, where −A generates an analytic semigroup and µ(u) is a Banach space valued measure depending on the solution. Then it is shown that the general theorems apply to a variety of semilinear parabolic boundary value problems involving measures in the interior and on the boundary of the domain. These results extend far beyond the known results in this field. A particularly new feature is the fact that the measures may depend nonlinearly and possibly nonlocally on the solution.

Abstract

A detailed study of abstract semilinear evolution equations of the form u + Au = µ(u) is undertaken, where −A generates an analytic semigroup and µ(u) is a Banach space valued measure depending on the solution. Then it is shown that the general theorems apply to a variety of semilinear parabolic boundary value problems involving measures in the interior and on the boundary of the domain. These results extend far beyond the known results in this field. A particularly new feature is the fact that the measures may depend nonlinearly and possibly nonlocally on the solution.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:03 Dec 2023 02:41
Publisher:American Mathematical Society
ISSN:0002-9947
Additional Information:First published in [Trans. Amer. Math. Soc. 356 (2004), no. 3], published by the American Mathematical Society
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1090/S0002-9947-03-03440-8
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1984467
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1072.35094