Global classical solutions to the elastodynamic equations with damping

Abstract In this paper, we show the global existence of classical solutions to the incompressible elastodynamics equations with a damping mechanism on the stress tensor in dimension three for sufficiently small initial data on periodic boxes, that is, with periodic boundary conditions. The approach...

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Main Authors:	Mengmeng Liu, Xueyun Lin
Format:	Article
Language:	English
Published:	SpringerOpen 2021-05-01
Series:	Journal of Inequalities and Applications
Subjects:	Elastodynamics Global classical solution Time-weighted energy estimate Damping mechanism
Online Access:	https://doi.org/10.1186/s13660-021-02608-9

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spelling	doaj-154f5771f2264286be38c1d3f14f9d4b2021-05-09T11:03:44ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-05-012021111510.1186/s13660-021-02608-9Global classical solutions to the elastodynamic equations with dampingMengmeng Liu0Xueyun Lin1College of Mathematics and Computer Science, Fuzhou UniversityCollege of Mathematics and Computer Science, Fuzhou UniversityAbstract In this paper, we show the global existence of classical solutions to the incompressible elastodynamics equations with a damping mechanism on the stress tensor in dimension three for sufficiently small initial data on periodic boxes, that is, with periodic boundary conditions. The approach is based on a time-weighted energy estimate, under the assumptions that the initial deformation tensor is a small perturbation around an equilibrium state and the initial data have some symmetry.https://doi.org/10.1186/s13660-021-02608-9ElastodynamicsGlobal classical solutionTime-weighted energy estimateDamping mechanism
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mengmeng Liu Xueyun Lin
spellingShingle	Mengmeng Liu Xueyun Lin Global classical solutions to the elastodynamic equations with damping Journal of Inequalities and Applications Elastodynamics Global classical solution Time-weighted energy estimate Damping mechanism
author_facet	Mengmeng Liu Xueyun Lin
author_sort	Mengmeng Liu
title	Global classical solutions to the elastodynamic equations with damping
title_short	Global classical solutions to the elastodynamic equations with damping
title_full	Global classical solutions to the elastodynamic equations with damping
title_fullStr	Global classical solutions to the elastodynamic equations with damping
title_full_unstemmed	Global classical solutions to the elastodynamic equations with damping
title_sort	global classical solutions to the elastodynamic equations with damping
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2021-05-01
description	Abstract In this paper, we show the global existence of classical solutions to the incompressible elastodynamics equations with a damping mechanism on the stress tensor in dimension three for sufficiently small initial data on periodic boxes, that is, with periodic boundary conditions. The approach is based on a time-weighted energy estimate, under the assumptions that the initial deformation tensor is a small perturbation around an equilibrium state and the initial data have some symmetry.
topic	Elastodynamics Global classical solution Time-weighted energy estimate Damping mechanism
url	https://doi.org/10.1186/s13660-021-02608-9
work_keys_str_mv	AT mengmengliu globalclassicalsolutionstotheelastodynamicequationswithdamping AT xueyunlin globalclassicalsolutionstotheelastodynamicequationswithdamping
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Global classical solutions to the elastodynamic equations with damping

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