Karolina Wielgos
supervisor: Krzysztof Chełmiński
The aim of my presentation is to roughly show my work on a thermo-visco-elastic model with non-linear damping forces and `L^1` temperature data. I plan to start with showing from which field of mathematics my problem comes and refer to its physical aspects. I will present the equations which describe thermo-visco-elastic effects in the materials with proper initial and boundary conditions and their physical derivation. I will also note that model is thermodynamically consistent.
My system depends on the temperature that enters the mechanical part both in the elastic constitutive equations and in describing the evolution of visco-elastic strain. This fact determines the steps of the proof of the existence of the solutions. I will show the proposed two-level Galerkin approximation and explain why two levels are needed. Thanks to this I can obtain a non-negativity of temperature in the entire deformation process, what is a crucial aspect. I plan to present the shortened proof of this feature. I also assume that initial temperature data is only of `L^1`-regularity, so I have to use Boccardo-Gallouet’s approach to obtain proper estimations. I will show the idea of this method based on my system.
Eventually, I will finish with the summary of the obtained solutions. The regularities of the displacement, elastic stress tensor and temperature will be noted. Additionally, I will mention further steps of the work on the topic which I will analyze later during my PhD studies.