Global Solutions to Repulsive Hookean Elastodynamics

Xianpeng Hu, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

The global existence of classical solutions to the three dimensional repulsive Hookean elastodynamics around an equilibrium is considered. By linearization and Hodge’s decomposition, the compressible part of the velocity, the density, and the compressible part of the transpose of the deformation gradient satisfy Klein–Gordon equations with speed (Formula presented.), while the incompressible parts of the velocity and of the transpose of the deformation gradient satisfy wave equations with speed one. The space-time resonance method combined with the vector field method is used in a novel way to obtain the decay of the solution and hence global existence.

Original languageEnglish (US)
Pages (from-to)1-48
Number of pages48
JournalArchive for Rational Mechanics and Analysis
DOIs
StateAccepted/In press - Aug 25 2016

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Transpose
Elastodynamics
Global Solution
Global Existence
Hodge Decomposition
Gradient
Klein-Gordon Equation
Combined Method
Wave equations
Classical Solution
Linearization
Wave equation
Vector Field
Space-time
Decay
Decomposition
Three-dimensional

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

Global Solutions to Repulsive Hookean Elastodynamics. / Hu, Xianpeng; Masmoudi, Nader.

In: Archive for Rational Mechanics and Analysis, 25.08.2016, p. 1-48.

Research output: Contribution to journalArticle

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