Global-in-time regular unique solutions with positive temperature to one-dimensional thermoelasticity
P Michał Bies, T Cieślak - SIAM Journal on Mathematical Analysis, 2023 - SIAM
We construct a unique regular solution to the minimal nonlinear system of one-dimensional
thermoelasticity. The obtained solution has a positive temperature. Our approach is based …
thermoelasticity. The obtained solution has a positive temperature. Our approach is based …
Decay of solutions of non-homogenous hyperbolic equations
PM Bies - arXiv preprint arXiv:2406.10592, 2024 - arxiv.org
We consider conditions for the decay in time of solutions of non-homogenous hyperbolic
equations. It is proven that solutions of the equations go to $0 $ in $ L^ 2$ at infinity if and …
equations. It is proven that solutions of the equations go to $0 $ in $ L^ 2$ at infinity if and …
Time-asymptotics of a heated string
PM Bies, T Cieślak - arXiv preprint arXiv:2405.04310, 2024 - arxiv.org
In the present paper, we study a model of a thermoelastic string that is initially heated. We
classify all the possible asymptotic states when time tends to infinity of such a model …
classify all the possible asymptotic states when time tends to infinity of such a model …
Global weak solutions in nonlinear 3D thermoelasticity
T Cieślak, B Muha, S Trifunović - Calculus of Variations and Partial …, 2024 - Springer
Here we study a nonlinear thermoelasticity hyperbolic-parabolic system describing the
balance of momentum and internal energy of a heat-conducting elastic body, preserving the …
balance of momentum and internal energy of a heat-conducting elastic body, preserving the …
On a thermo‐visco‐elastic model with nonlinear damping forces and L1 temperature data
S Owczarek, K Wielgos - Mathematical Methods in the Applied …, 2023 - Wiley Online Library
The aim of this paper is to prove the existence of weak solutions to thermo‐visco‐elastic
system of equations. In considered problem, the temperature term is included in the elastic …
system of equations. In considered problem, the temperature term is included in the elastic …