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Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations

Schimperna, G and Zelik, S (2010) Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations arXiv. (Unpublished)

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Abstract

A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by using a regularization procedure and deducing suitable a-priori estimates. If a viscosity term is added and additional conditions on the nonlinear terms are assumed, then it is proved that any weak solution becomes instantaneously strictly positive. This in particular implies uniqueness for strictly positive times and further time-regularization properties. The long-time behavior of the problem is also investigated and the existence of trajectory attractors and, under more restrictive conditions, of strong global attractors is shown.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Schimperna, GUNSPECIFIEDUNSPECIFIED
Zelik, SUNSPECIFIEDUNSPECIFIED
Date : 16 September 2010
Related URLs :
Additional Information : This is an arXiv version of this paper.
Depositing User : Symplectic Elements
Date Deposited : 20 Jan 2015 10:29
Last Modified : 10 Apr 2015 13:33
URI: http://epubs.surrey.ac.uk/id/eprint/806854

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