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

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

Type of Publication: Working Paper/Technical Report
Publication status: Submitted
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-2-8ztzhsco3jj82
Author: Racke, Reinhard; Said-Houari, Belkacem
Year of publication: 2019
Series: Konstanzer Schriften in Mathematik ; 382
Summary:
In this paper, we consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan-Moore-Gibson-Thompson equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. First, using the contraction mapping theorem, we show a local existence result in appropriate function spaces. Second, by using the energy method together with a bootstrap argument, we prove a global existence result for small data. Third, polynomial decay rates in time for the solution will be obtained for space dimensions N >=2.
Subject (DDC): 510 Mathematics
Link to License: In Copyright
Bibliography of Konstanz: Yes

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RACKE, Reinhard, Belkacem SAID-HOUARI, 2019. Global well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equation

@techreport{Racke2019Globa-45479, series={Konstanzer Schriften in Mathematik}, title={Global well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equation}, year={2019}, number={382}, author={Racke, Reinhard and Said-Houari, Belkacem} }

Racke, Reinhard Said-Houari, Belkacem Racke, Reinhard 2019-03-15T08:56:19Z eng Global well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equation terms-of-use In this paper, we consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan-Moore-Gibson-Thompson equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. First, using the contraction mapping theorem, we show a local existence result in appropriate function spaces. Second, by using the energy method together with a bootstrap argument, we prove a global existence result for small data. Third, polynomial decay rates in time for the solution will be obtained for space dimensions N >=2. 2019-03-15T08:56:19Z Said-Houari, Belkacem 2019

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