Local strong solutions in a quasilinear Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard linear solid

Abstract This manuscript is concerned with the evolution system $$\begin{aligned} \left\{ \begin{array}{l}u_{ttt} + \alpha u_{tt} = \big (\gamma (\Theta ) u_{xt}\big )_x + \big ( \widehat{\gamma }(\Theta ) u_x\big )_x, \\ \Theta _t = D \Theta _{xx} + \Gamma (\Theta ) u_{xt}^2, \end{array} \right. \end{aligned}$$ u ttt + α u tt = ( γ ( Θ ) u xt ) x + ( γ ^ ( Θ ) u x ) x , Θ t = D Θ xx + Γ ( Θ ) u xt 2 , which arises as a simplified model for heat generation during acoustic wave propagation in a one-dimensional viscoelastic medium of standard linear solid type. Under the assumptions that $$D>0$$ D > 0 and $$\alpha \ge 0$$ α ≥ 0 , and that $$\gamma , \widehat{\gamma }$$ γ , γ ^ and $$\Gamma $$ Γ