Magneto-elastic waves and disturbances in initially stressed conducting media: II

R. G. Roy; P. R. Sengupta

doi:10.1007/bf00876774

Magneto-elastic waves and disturbances in initially stressed conducting media: II

Pure and Applied Geophysics ◽

10.1007/bf00876774 ◽

1972 ◽

Vol 101 (1) ◽

pp. 54-66

Author(s):

R. G. Roy ◽

P. R. Sengupta

Keyword(s):

Elastic Waves ◽

Stressed Conducting

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Magneto-thermo-visco-elastic waves in an initially stressed conducting layer

Sadhana ◽

10.1007/bf02745739 ◽

1998 ◽

Vol 23 (3) ◽

pp. 233-246 ◽

Cited By ~ 3

Author(s):

Amit Kumar Rakshit ◽

P R Sengupta

Keyword(s):

Elastic Waves ◽

Conducting Layer ◽

Stressed Conducting

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Magneto-elastic waves and disturbances in initially stressed conducting media

Pure and Applied Geophysics ◽

10.1007/bf00875220 ◽

1972 ◽

Vol 93 (1) ◽

pp. 41-54 ◽

Cited By ~ 14

Author(s):

S. N. De ◽

P. R. Sengupta

Keyword(s):

Elastic Waves ◽

Stressed Conducting

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Magneto-elastic waves in an initially stressed conducting elastic layer

Pure and Applied Geophysics ◽

10.1007/bf00875263 ◽

1972 ◽

Vol 99 (1) ◽

pp. 55-60

Author(s):

Saurendra Nath De

Keyword(s):

Elastic Waves ◽

Elastic Layer ◽

Stressed Conducting

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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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