Well-Posedness of the Green–Lindsay Variational Problem of Dynamic Thermoelasticity

Chyr, І. А.; Shynkarenko, H. А.

doi:10.1007/s10958-017-3515-0

Cited by 6 publications

(1 citation statement)

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“…Among the works elaborated for this purpose, it is considered that the papers of Mindlin [10], of Green and Rivlin [11], and the book Gurtin et al [12] are very relevant from this regards. Other aspects of the bodies with dipolar structure are addressed in the studies [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. In [14], the authors introduced the coupled theory, the Lord-Schulman theory with one relaxation time and the Green-Lindsay theory with two relaxation times to study the influence of the magnetic field and rotation on the 2-D problem of a fiber-reinforced thermoelastic body and the interaction with each other under the influence of gravity.…”

Section: Introductionmentioning

confidence: 99%

Some Results in Green–Lindsay Thermoelasticity of Bodies with Dipolar Structure

2020

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The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive.

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