4 papers
Entropy-energy solutions for Thermo-Visco-Elastic systems with Mróz-type inelastic behavior
Tomasz CieÅlak, Sebastian Owczarek, Karolina Wielgos
In this article, we study a thermodynamically consistent thermo-visco-elastic model describing the balance of internal energy in a heat-conducting inelastic body. In the considered…
Rate of convergence to equilibrium for the heated string
Tomasz CieÅlak, Jacek Jendrej, Christian Stinner
In the present manuscript, we calculate the exponential rate of convergence of the heated string system (a mixed-type hyperbolic-parabolic system of PDEs) towards the equilibrium,…
Existence, uniqueness, and long-time asymptotic behavior of regular solutions in multidimensional thermoelasticity
Piotr MichaÅ Bies, Tomasz CieÅlak, Mario Fuest +3
We study a simplified nonlinear thermoelasticity model on two- and three-dimensional tori. A novel functional involving the Fisher information associated with temperature is introd…
Uniqueness problem for Prandtl spirals
Tomasz CieÅlak, Piotr Kokocki, PrzemysÅaw Kosewski
In this paper, we study the problem of uniqueness of a divergence-free velocity field with vorticity given by the Prandtl spiral. We show that if the class of admissible velocities…