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On radial stationary solutions to a model of non-equilibrium growth

Published online by Cambridge University Press:  16 January 2013

CARLOS ESCUDERO ,
ROBERT HAKL ,
IRENEO PERAL  and
PEDRO J. TORRES
CARLOS ESCUDERO
Affiliation:
Departamento de Matemáticas & ICMAT (CSIC-UAM-UC3M-UCM), Universidad Autónoma de Madrid, E-28049 Madrid, Spain email: cel@icmat.es
ROBERT HAKL
Affiliation:
Institute of Mathematics, AS CR, Žižkova 22, 616 62 Brno, Czech Republic
IRENEO PERAL
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
PEDRO J. TORRES
Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, E-18071 Granada, Spain
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Abstract

We present the formal geometric derivation of a non-equilibrium growth model that takes the form of a parabolic partial differential equation. Subsequently, we study its stationary radial solutions by means of variational techniques. Our results depend on the size of a parameter that plays the role of the strength of forcing. For small forcing we prove the existence and multiplicity of solutions to the elliptic problem. We discuss our results in the context of non-equilibrium statistical mechanics.

Keywords

non-equilibrium growthradial solutionsvariational methodsboundary value problems
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 3 , June 2013 , pp. 437 - 453
Copyright
Copyright © Cambridge University Press 2013

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