A model in one-dimensional thermoelasticity. (March 2022)

• Record Type: Journal Article
• Authors: Cieślak, Tomasz; Galić, Marija; Muha, Boris
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: Thermoelasticity -- Strong solution -- Weak solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112703
• Languages: English
• ISSNs: 0362-546X

Abstract

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.