Publikation: Global well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equation
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2019
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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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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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<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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