LONG-TIME BEHAVIOUR OF A THERMOMECHANICAL MODEL FOR ADHESIVE CONTACT

被引：9

作者：

Bonetti, Elena ^{[1
]}

Bonfanti, Giovanna ^{[2
]}

Rossi, Riccarda ^{[2
]}

机构：

[1] Univ Pavia, Dipartimento Matemat F Casorati, Via Ferrata 1, I-27100 Pavia, Italy

[2] Univ Brescia, Dipartimento Matemat, I-25133 Brescia, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2011年 / 4卷 / 02期

关键词：

Nonlinear PDE system; contact with adhesion; long-time behaviour;

D O I：

10.3934/dcdss.2011.4.273

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the large-time analysis of a PDE system modelling contact with adhesion, in the case when thermal effects are taken into account. The phenomenon of adhesive contact is described in terms of phase transitions for a surface damage model proposed by M. FREMOND. Thermal effects are governed by entropy balance laws. The resulting system is highly nonlinear, mainly due to the presence of internal constraints on the physical variables and the coupling of equations written in a domain and on a contact surface. We prove existence of solutions on the whole time interval (0, +infinity) by a double approximation procedure. Hence, we are able to show that solution trajectories admit cluster points which fulfil the stationary problem associated with the evolutionary system, and that in the large-time limit dissipation vanishes.

引用

页码：273 / 309

页数：37

共 18 条

[1]

[Anonymous], 1973, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert

[2]

[Anonymous], 1992, Japan J. Indust. Appl. Math.

[3]

Barbu V, 1976, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste Romania

[4] A phase field model with thermal memory governed by the entropy balance [J].