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

Carlos Lizama and Marina Murillo-Arcila
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Carlos Lizama: Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago 9160000, Chile
Marina Murillo-Arcila: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, Spain

Mathematics, 2020, vol. 8, issue 10, 1-9

Abstract: 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.

Keywords: well-posedness; Moore–Gibson–Thompson equation; degenerate evolution equations; R-boundedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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