Local and Global Solvability in a Viscous Wave Equation Involving General Temperature-Dependence
Year: 2025
Type: article
Abstract: The present manuscript studies a coupled thermoelastic-viscoelastic system, modelling the interaction between mechanical displacement and temperature in viscoelastic materials in a bounded interval. This topic is of interest in the fields of applied mathematics and continuum mechanics. The system under consideration reads $$\begin{aligned} \left \{ \textstyle\begin{array}{l} u_{tt} = (\gamma (\Theta ) u_{xt})_{x} + (\tilde {\gamma }(\Theta ) u_{x})_{x}+(f( \Theta ))_{x}, \\ \Theta _{t} = D\Theta _{xx} + \Gamma (\Theta ) u_{xt}^{2}+F(\Theta )u_{xt}, \end{array}\displaystyle \right . \end{aligned}$$ { u t t = ( γ ( Θ ) u x t ) x + ( γ ˜ ( Θ ) u x ) x + ( f ( Θ ) ) x , Θ t = D Θ x x + Γ ( Θ ) u x t 2 + F ( Θ ) u x t , in an open bounded interval, which with $\gamma \equiv \tilde {\gamma }\equiv \Gamma $ γ ≡ γ ˜ ≡ Γ as well as $f\equiv F$ f ≡ F reduces to the classical model for the evolution of strains and temperatures in thermoviscoelasticity. In contrast to the preceding related studies, the present study focuses on situations in which not only $f$ f and $F$ F , but also the core components $\gamma $ γ , $\tilde {\gamma }$ γ ˜
Source: Acta Applicandae Mathematicae
Author: Torben J. Fricke
Institution: Paderborn University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4415570819