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Global Well-Posedness and Finite-Time Blow-Up of Some Heat-Type Equations

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  02 November 2016

Tarek Saanouni
Tarek Saanouni*
Affiliation:
Qassim University, Faculty of Science and Literature of Uqlat Assgoor, Al-Qaseem, Saudi Arabia (tarek.saanouni@ipeiem.rnu.tn)
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Abstract

We study two different heat-type equations. First, global well-posedness in the energy space of some high-order semilinear heat-type equation with exponential nonlinearity is obtained for even space dimensions. Second, a finite-time blow-up result for the critical monomial focusing heat equation with the p-Laplacian is proved.

Keywords

high-order heat-type equationitalicp/italic-Laplacian parabolic equationStrichartz estimateMoser–Trudinger inequalitywell-posedness

MSC classification

Secondary: 35Q55: NLS-like equations (nonlinear Schrödinger)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 2 , May 2017 , pp. 481 - 497
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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