Lp-Lq-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains

We examine the Cauchy problem for a model of linear acoustics, called the Moore–Gibson–Thompson equation, describing a sound propagation in thermo-viscous elastic media with two temperatures on cylindrical domains. For an adequate combination of the parameters of the model we prove Lp-Lq-well-posedness, and we provide maximal regularity estimates which are optimal thanks to the theory of operator-valued Fourier multipliers.