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Mathematical analysis of some model in
Leszek Bartczak
Faculty of Mathematics and Information Science,
Warsaw University of Technology,
ul. Koszykowa 75, 00-662 Warsaw, Poland
[email protected]
We consider the viscoplasticity equations coupled with the heat equation. This model
describes a phenomena in a deformed metal additionally exposed to a heat modification.
On the one hand the temperature ”controls” the domain of an elastic behaviour of the
body, on the other hand the strain and the stress appearing in the body influences the
heat conduction. We prove the existence and the uniqueness of the solution to the model
in the case of a small deformation. See [1] and [2].
Keywords: continuum mechanics, viscoplastic deformation, heat conduction, thermovisco-plasticity.
[1] L. Bartczak, Mathematical analysis of a thermo-visco-plastic model with Bodner Partom constitutive equations, J. Math. Anal. Appl., 385 (2012), 961–974.
[2] L. Bartczak, On existence of global in time solutions to thermoelasticity with a
quadratic nonlinearity for small data, Accepted to Topological Methods in Nonlinear Analysis.
[3] L. Bartczak, Analiza matematyczna równań termolepkoplastyczności, Ph.D. thesis on
Warsaw University of Technology.