Well-posedness of a stress-augmented Moore-Gibson-Thompson-type model for thermoviscoelastic evolution in a standard linear solid

This manuscript studies a coupled system of nonlinear parabolic and hyperbolic equations that models thermoviscoelastic materials with explicit internal stress relaxation, $$\{\begin{array}{l}\tau u_{ttt}+u_{tt}=(D(\mathrm{\Theta })u_{xt}{)}_x+(C(\mathrm{\Theta })u_x{)}_x,\\ {\mathrm{\Theta }}_t={\mathrm{\Theta }}_{xx}+\mathrm{\mid }E(\mathrm{\Theta })u_{xt}+F(\mathrm{\Theta })g_t{\mathrm{\mid }}^2,\\ \tau g_t+g=D(\mathrm{\Theta })u_{xt}+C(\mathrm{\Theta })u_x\mathrm{.}\end{array}$$ 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 $\tau >0$ and that $D,C\in C^2([0,\mathrm{\infty }))$ are positive and $E,F\in C^1([0,\mathrm{\infty }))$, 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.