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 $${aligned} \{ {array}{l}uₜₜₜ + α uₜₜ = (γ (Θ ) uₓₜ )_x + ( {γ }(Θ ) u_x )_x, \\ Θ _t = D Θ ₓₓ + Γ (Θ ) uₓₜ^2, {array} . {aligned}$$ 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 α ≥ 0 α ≥ 0 , and that γ , γ γ , γ ^ and Γ Γ