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

This manuscript is concerned with the evolution system $$\{\begin{array}{l}{u}_{ttt}+\alpha u_{tt}=(\gamma (\mathrm{\Theta })u_{xt}{)}_x+(\widehat{\gamma }(\mathrm{\Theta })u_x{)}_x,{\mathrm{\Theta }}_t=D{\mathrm{\Theta }}_{xx}+\mathrm{\Gamma }(\mathrm{\Theta })u_{xt}^2,\end{array}$$ 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 $D>0$ and $\alpha \ge 0$, and that $\gamma ,\widehat{\gamma }$ and $\mathrm{\Gamma }$ are sufficiently smooth with $\gamma >0,\widehat{\gamma }>0$ and $\mathrm{\Gamma }\ge 0$ on $[0,\mathrm{\infty })$, for suitably regular initial data a statement on local existence and uniqueness of solutions in an associated Neumann problem is derived in a suitable framework of strong solvability.