Global existence for certain fourth order evolution equations

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URI: https://hdl.handle.net/10902/34401
ISSN: 1553-5258
ISSN: 1534-0392
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Autoría
Granero Belinchón, RafaelAutoridad Unican; Magliocca, Martina
Fecha
2024-11
Derechos
© American Institute of Mathematical Sciences. This article has been accepted for publication in a revised form in Communications on Pure and Applied Analysis (CPAA), https://www.aimsciences.org/cpaa. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.
Publicado en
Communications on Pure and Applied Analysis, 2024, 23(11), 1646-1660
Editorial
AIMS Press
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Palabras clave
Higher order parabolic equations
Global solutions
Epitaxial growth
Thin films
Resumen/Abstract
In this paper we established three global in time results for two fourth order nonlinear parabolic equations. The first of such equations involved the Hessian and appeared in epitaxial growth. For such an equation, we gave conditions ensuring the global existence of the solution. For certain regime of the parameters, our size condition involved the norm in a critical space with respect to the scaling of the equation and improved previous existing results in the literature for this equation. The second of the equations under study was a thin film equation with a porous medium nonlinearity. For this equation, we established conditions leading to the global existence of the solution.
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