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

Racke, Reinhard; Said-Houari, Belkacem

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

Files

Racke_2-8ztzhsco3jj82.pdf(554.74 KB)

Date

2019

Authors

Racke, Reinhard

Said-Houari, Belkacem

Series

Konstanzer Schriften in Mathematik; 382

Publication type

Working Paper/Technical Report

Publication status

Submitted

Abstract

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

Cite This

ISO 690

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

BibTex

@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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Yes