L-p-L-q-Well Posedness for the Moore-Gibson-Thompson Equation with Two Temperatures on Cylindrical Domains

[EN] 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 L-p-L-q-well-posedness, and we provide maximal regularity estimates which are optimal thanks to the theory of operator-valued Fourier multipliers.