@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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    <dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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