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Quasilinear parabolic problems via maximal regularity


Amann, H (2005). Quasilinear parabolic problems via maximal regularity. Advances in Differential Equations, 10(10):1081-1110.

Abstract

We use maximal Lp regularity to study quasilinear parabolic
evolution equations. In contrast to all previous work we only assume that the nonlinearities are defined on the space in which the solution is sought for. It is shown that there exists a unique maximal solution depending continuously on all data, and criteria for global existence are given as well. These general results possess numerous applications, some of which will be discussed in separate publications.

Abstract

We use maximal Lp regularity to study quasilinear parabolic
evolution equations. In contrast to all previous work we only assume that the nonlinearities are defined on the space in which the solution is sought for. It is shown that there exists a unique maximal solution depending continuously on all data, and criteria for global existence are given as well. These general results possess numerous applications, some of which will be discussed in separate publications.

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24 citations in Scopus®
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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
Language:English
Date:2005
Deposited On:01 Feb 2010 08:19
Last Modified:06 Dec 2017 20:45
Publisher:Khayyam
ISSN:1079-9389
Official URL:http://www.aftabi.com/ADE/ade10.html
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2162362

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