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Mathematical analysis of some model in thermoviscoplasticity Leszek Bartczak Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland [email protected] Abstract 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. References [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.
