Title

A parabolic integro-differential equation arising from thermoelastic contact

Keywords

Integro-differential; Non-local; Parabolic; Thermoelastic contact

Abstract

In this paper we consider a class of integro-differential equations of parabolic type arising in the study of a quasi-static thermoelastic contact problem involving a critical parameter α. For α < 1, the problem is first transformed into an equivalent standard parabolic equation with non-local and non-linear boundary conditions. Then the existence, uniqueness and continuous dependence of the solution upon the data are demonstrated via solution representation techniques and the maximum principle. Finally the asymptotic behavior of the solution as t → ∞ is examined, and we show that the non-local term has no impact on the asymptotic behavior for α < 1. The paper concludes with some remarks on the case α > 1.

Publication Date

1-1-1997

Publication Title

Discrete and Continuous Dynamical Systems

Volume

3

Issue

2

Number of Pages

217-234

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.3934/dcds.1997.3.217

Socpus ID

0031499325 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0031499325

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