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Global existence and decay to equilibrium for some crystal surface models

Abstract: ABSTRACT: In this paper we study the large time behavior of the solutions to the following nonlinear fourth-order equations ?tu=?e??u,?tu=?u2?2(u3). ?tu=?e??u,?tu=?u2?2(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.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Discrete and continuous dynamical systems, Volume 39, Number 4, April 2019, pp. 2101-2131

Editorial: American Institute of Mathematical Sciences

 Año de publicación: 2019

Nº de páginas: 31

Tipo de publicación: Artículo de Revista

 DOI: 10.3934/dcds.2019088

ISSN: 1553-5231,1078-0947

Url de la publicación: http://dx.doi.org/10.3934/dcds.2019088