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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Carlos Lizama & Marina Murillo-Arcila, 2020. "L p - L q -Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains," Mathematics, MDPI, vol. 8(10), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1748-:d:426462
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