On a contact problem in thermoelasticity with second sound

Sprenger, Jan

On a contact problem in thermoelasticity with second sound

Files

research_paper_245.pdf(387.84 KB)

Date

2008

Authors

Sprenger, Jan

Series

Konstanzer Schriften in Mathematik und Informatik; 245

Publication type

Preprint

Abstract

We investigate the existence and stability of a thermoelastic contact problem with second sound. Previous results established the existence and stability of a solution of the corresponding classical system in the case of radial symmetry. However, recent works have shown that sometimes stability can be lost when the classical Fourier heat conduction is substituted by Cattaneo's Law. We show that also in this case this substitution does indeed lead to a loss in regularity that proves to be a major problem prohibiting the transfer of the existence proof for the classical problem to the problem with second sound, leaving the existence of a solution an open question. We then prove that, if a viscoelastic term is added to the equations providing additional regularity, existence and exponential stability - the second, as can be expected, only in the case of radial symmetry - follow.

Subject (DDC)

510 Mathematics

Keywords

thermoelasticity,contact problem,long term behaviour

Cite This

ISO 690

SPRENGER, Jan, 2008. On a contact problem in thermoelasticity with second sound

BibTex

@unpublished{Sprenger2008conta-659,
  year={2008},
  title={On a contact problem in thermoelasticity with second sound},
  author={Sprenger, Jan}
}

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