# 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.

## 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.

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## Additional indexing

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2005 29 Jan 2010 12:36 05 Apr 2016 13:24 Izdatel'stvo Nauka 0042-1316 https://doi.org/10.1070/RM2005v060n06ABEH004279 http://mi.mathnet.ru/eng/umn1674 http://www.iop.org/EJ/abstract/0036-0279/60/6/R03

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