Global existence and decay to equilibrium for some crystal surface models

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URI: http://hdl.handle.net/10902/15992
ISSN: 1553-5231
ISSN: 1078-0947
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Autoría
Granero Belinchón, RafaelAutoridad Unican; Magliocca, Martina
Fecha
2019
Derechos
© American Institute of Mathematical Sciences. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series A following peer review. The definitive publisher-authenticated version Discrete and continuous dynamical systems - Series A, Volume 39, Number 4, April 2019, pp. 2101-2131 is available online at: http://dx.doi.org/10.3934/dcds.2019088
Publicado en
Discrete and continuous dynamical systems, Volume 39, Number 4, April 2019, pp. 2101-2131
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American Institute of Mathematical Sciences
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Palabras clave
Crystal surface model
Nonlinear fourth-order parabolic equations
Global existence
Decay to equilibrium
Resumen/Abstract
ABSTRACT: In this paper we study the large time behavior of the solutions to the following nonlinear fourth-order equations @tu=Δe-Δu;@tu=-u2Δ2(u3) These two PDE were proposed as models of the evolution of crystal surfaces by J. Krug, H.T. Dobbs, and S. Majaniemi (Z. Phys. B, 97,281-291, 1995) and H. Al Hajj Shehadeh, R. V. Kohn, and J. Weare (Phys. D, 240, 1771-1784, 2011), respectively. In particular, we find explicitly computable conditions on the size of the initial data (measured in terms of the norm in a critical space) guaranteeing the global existence and exponential decay to equilibrium in the Wiener algebra and in Sobolev spaces
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