A model in one-dimensional thermoelasticity
Analysis of PDEs
2020-05-29 v2
Abstract
We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local-in-time strong solution. Also, some global-in-time weak measure valued solutions are proven to exist. To this end we introduce an auxiliary problem with artificial viscosity and prove its global-in-time well-posedness. Next, we show that solutions of the auxiliary problem converge, at some short time interval to the strong solution, and to our measure valued solution for an arbitrary time.
Cite
@article{arxiv.2003.03806,
title = {A model in one-dimensional thermoelasticity},
author = {Tomasz Cieslak and Marija Galić and Boris Muha},
journal= {arXiv preprint arXiv:2003.03806},
year = {2020}
}