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Non-local quasilinear parabolic equations


Amann, H (2005). Non-local quasilinear parabolic equations. Uspekhi Matematicheskikh Nauk, 60(6(366)):21-32.

Abstract

This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal $L_p$ regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona–Malik equation of image processing.

This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal $L_p$ regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona–Malik equation of image processing.

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5 citations in Web of Science®
5 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:29 Jan 2010 12:36
Last Modified:05 Apr 2016 13:24
Publisher:Izdatel'stvo Nauka
ISSN:0042-1316
Publisher DOI:10.1070/RM2005v060n06ABEH004279
Official URL:http://mi.mathnet.ru/eng/umn1674
Related URLs:http://www.iop.org/EJ/abstract/0036-0279/60/6/R03
Permanent URL: http://doi.org/10.5167/uzh-21656

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