Well-posedness of a stress-augmented Moore-Gibson-Thompson-type model for thermoviscoelastic evolution in a standard linear solid
Abstract
This manuscript studies a coupled system of nonlinear parabolic and hyperbolic equations that models thermoviscoelastic materials with explicit internal stress relaxation, τuttt + utt = (D(Θ)uxt)x + (C(Θ)ux)x, Θt = Θxx + |E(Θ)uxt + F(Θ)gt|2, τgt + g = D(Θ)uxt + C(Θ)ux. The system arises from a stress-strain constitutive relation of Zener type, where the internal variable g encodes mechanical memory effects. A key feature is the explicit coupling of stress relaxation to the heat equation through the dissipation term, which differs from standard approaches that eliminate g via algebraic substitution. Under the assumptions that τ>0 and that D,C∈ C2([0,∞)) are positive and E,F∈ C1([0,∞)), and for suitably regular initial data, we establish local existence and uniqueness of strong solutions. Under additionally strengthened regularity requirements on the initial data and on D,C, this solution is moreover shown to be classical. These results extend a corresponding local strong and classical solvability theory developed for the underlying system without the stress variable g to the present, stress-augmented setting.
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BibTeX
@misc{fricke2026wellposedness,
title = {{Well-posedness of a stress-augmented Moore-Gibson-Thompson-type model for thermoviscoelastic evolution in a standard linear solid}},
author = {Torben Fricke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31134},
eprint = {2610.31134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31134},
}
RIS
TY - UNPB
TI - Well-posedness of a stress-augmented Moore-Gibson-Thompson-type model for thermoviscoelastic evolution in a standard linear solid
AU - Torben Fricke
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31134
UR - https://arxiv.org/abs/2610.31134
AB - This manuscript studies a coupled system of nonlinear parabolic and hyperbolic equations that models thermoviscoelastic materials with explicit internal stress relaxation, τu_ttt + u_tt = (D(Θ)u_xt)_x + (C(Θ)u_x)_x, Θ_t = Θ_xx + |E(Θ)u_xt + F(Θ)g_t|^2, τg_t + g = D(Θ)u_xt + C(Θ)u_x. The system arises from a stress-strain constitutive relation of Zener type, where the internal variable g encodes mechanical memory effects. A key feature is the explicit coupling of stress relaxation to the heat equation through the dissipation term, which differs from standard approaches that eliminate g via algebraic substitution. Under the assumptions that τ>0 and that D,C∈ C^2([0,∞)) are positive and E,F∈ C^1([0,∞)), and for suitably regular initial data, we establish local existence and uniqueness of strong solutions. Under additionally strengthened regularity requirements on the initial data and on D,C, this solution is moreover shown to be classical. These results extend a corresponding local strong and classical solvability theory developed for the underlying system without the stress variable g to the present, stress-augmented setting.
ER -