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Preventing blow up by convective terms in dissipative PDEs.

Bilgen, B, Kalantarov, V and Zelik, S (2015) Preventing blow up by convective terms in dissipative PDEs. arXiv.

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Abstract

We study the impact of the convective terms on the global solvability or finite time blow up of solutions of dissipative PDEs. We consider the model examples of 1D Burger's type equations, convective Cahn-Hilliard equation, generalized Kuramoto-Sivashinsky equation and KdV type equations, we establish the following common scenario: adding sufficiently strong (in comparison with the destabilizing nonlinearity) convective terms to equation prevents the solutions from blowing up in finite time and makes the considered system globally well-posed and dissipative and for weak enough convective terms the finite time blow up may occur similarly to the case when the equation does not involve convective term. This kind of result has been previously known for the case of Burger's type equations and has been strongly based on maximum principle. In contrast to this, our results are based on the weighted energy estimates which do not require the maximum principle for the considered problem.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Bilgen, BUNSPECIFIEDUNSPECIFIED
Kalantarov, VUNSPECIFIEDUNSPECIFIED
Zelik, SUNSPECIFIEDUNSPECIFIED
Date : 13 September 2015
Uncontrolled Keywords : math.AP, math.AP, 35A01, 35B44, 35B45
Related URLs :
Additional Information : This is an arXiv version of the paper. arXiv:1509.03845 [math.AP]
Depositing User : Symplectic Elements
Date Deposited : 24 Feb 2016 10:20
Last Modified : 24 Feb 2016 10:20
URI: http://epubs.surrey.ac.uk/id/eprint/809934

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