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

被引：23

作者：

Escudero, Carlos ^{[1
,2
]}

Hakl, Robert ^{[3
]}

Peral, Irene ^{[1
]}

Torres, Pedro J. ^{[4
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] Univ Autonoma Madrid, ICMAT, CSIC UAM UC3M UCM, E-28049 Madrid, Spain

[3] AS CR, Inst Math, Brno 61662, Czech Republic

[4] Univ Granada, Dept Matemat Aplicada, E-18071 Granada, Spain

来源：

EUROPEAN JOURNAL OF APPLIED MATHEMATICS | 2013年 / 24卷

关键词：

non-equilibrium growth; radial solutions; variational methods; boundary value problems; ELLIPTIC PROBLEMS; CURVATURE FLOW; REGULARITY; INTERFACES; CONTINUUM; GRADIENT;

D O I：

10.1017/S0956792512000484

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：437 / 453

页数：17

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