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