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Global well-posedness of the Cauchy problem for the 3D Jordan–Moore–Gibson–Thompson equation

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2021

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https://doi.org/10.1142/S0219199720500698
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Communications in Contemporary Mathematics. World Scientific Publishing. 2021, 23(07), 2050069. ISSN 0219-1997. eISSN 1793-6683. Available under: doi: 10.1142/S0219199720500698

Zusammenfassung

We consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan–Moore–Gibson–Thompson (JMGT) equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. We show a local existence result in appropriate function spaces, and, using the energy method together with a bootstrap argument, we prove a global existence result for small data, without using the linear decay. Finally, polynomial decay rates in time for a norm related to the solution will be obtained.

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510 Mathematik

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ISO 690RACKE, Reinhard, Belkacem SAID-HOUARI, 2021. Global well-posedness of the Cauchy problem for the 3D Jordan–Moore–Gibson–Thompson equation. In: Communications in Contemporary Mathematics. World Scientific Publishing. 2021, 23(07), 2050069. ISSN 0219-1997. eISSN 1793-6683. Available under: doi: 10.1142/S0219199720500698
BibTex
@article{Racke2021Globa-55439,
  year={2021},
  doi={10.1142/S0219199720500698},
  title={Global well-posedness of the Cauchy problem for the 3D Jordan–Moore–Gibson–Thompson equation},
  number={07},
  volume={23},
  issn={0219-1997},
  journal={Communications in Contemporary Mathematics},
  author={Racke, Reinhard and Said-Houari, Belkacem},
  note={Article Number: 2050069}
}
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