Global smooth solutions in a one-dimensional thermoviscoelastic model with temperature-dependent paramaters

This manuscript is concerned with the system \begin{align*} \left{ \begin{array}{l} u_{tt} = (γ(Θ) u_{xt})x + (a(x,t) u_x)x +(f(Θ))x, \[1mm] Θ_t = DΘ{xx} + γ(Θ) u{xt}^2 + f(Θ) u{xt}, \end{array} \right. \end{align*} which is used to describe thermoviscoelastic developments in one-dimensional Kelvin-Voigt materials. \abs It is assumed that $a,\gamma$ and $f$ are sufficiently smooth functions that satisfy $$c_{\gamma }<\gamma (\zeta )<C_{\gamma },{\gamma }^{\mathrm{\prime }\mathrm{\prime }}(\zeta )\le 0,f(0)=0,\mathrm{\mid }{f}^{\mathrm{\prime }}(\zeta )\mathrm{\mid }\le C_{f}and\mathrm{\mid }f(\zeta )\mathrm{\mid }\le C_f(1+\zeta {)}^{\alpha }forall\zeta \ge 0$$ and some positive constants $c_{\gamma },C_{\gamma },C_f>0$ and $\alpha \in (0,5\mathrm{/}6)$. Under these conditions, this study then establishes a result on the existence of global classical solutions for sufficiently smooth but arbitrarily large initial data.