Scattering Relations of Elastic Waves by a Multi-Layered Thermoelastic Body

Computational Mathematics and Variational Analysis - Springer Optimization and Its Applications ◽

10.1007/978-3-030-44625-3_1 ◽

2020 ◽

pp. 1-23

Author(s):

Evagelia S. Athanasiadou ◽

Vassilios Sevroglou ◽

Stefania Zoi

Keyword(s):

Elastic Waves ◽

Thermoelastic Body

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Scattering of elastic waves by a small thermoelastic body

International Journal of Engineering Science ◽

10.1016/0020-7225(94)90167-8 ◽

1994 ◽

Vol 32 (10) ◽

pp. 1593-1603 ◽

Cited By ~ 5

Author(s):

George Dassios ◽

Vassilis Kostopoulos

Keyword(s):

Elastic Waves ◽

Scattering Of Elastic Waves ◽

Thermoelastic Body

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Scattering theorems of elastic waves for a thermoelastic body

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.4051 ◽

2016 ◽

Vol 41 (3) ◽

pp. 998-1004 ◽

Cited By ~ 2

Author(s):

E. Athanasiadou ◽

V. Sevroglou ◽

S. Zoi

Keyword(s):

Elastic Waves ◽

Thermoelastic Body

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Remarks on nonlinear elastic waves with null conditions

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2020039 ◽

2020 ◽

Vol 26 ◽

pp. 121

Author(s):

Dongbing Zha ◽

Weimin Peng

Keyword(s):

Initial Data ◽

Global Existence ◽

Elastic Waves ◽

Wave Equations ◽

Alternative Proof ◽

Classical Solutions ◽

Small Initial Data ◽

Hyperelastic Materials ◽

Variational Structure ◽

Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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