Thermo-elasticity for Anisotropic Media in Higher Dimensions

Wirth, Jens

doi:10.1007/978-3-319-00125-8_17

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Remark 61 (Classical Thermodiffusion In Higher Dimensions)1

Some Concluding Remarks1

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2013

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“…The treatment of those models is more delicate than in 1D. The interested reader can find results for thermoelasticity in 2D in [15,16] and for 3D in [17] by generalizing the approach we followed in this paper. In [18], one can find results for nonlinear 3D models of thermodiffusion in a micropolar medium in bounded domains.…”

Section: Remark 61 (Classical Thermodiffusion In Higher Dimensions)mentioning

confidence: 98%

“…After including the diffusion effect, these models read as follows:

\begin{matrix} aligned \\ right U_{tt} + A MathClass-open(D MathClass-close) U + γ_{1} \nabla θ_{1} + γ_{2} \nabla θ_{2} & left = 0, & right \\ right c \frac{\partial θ_{1}}{∂t} - κΔ θ_{1} + γ_{1} \nabla^{T} U_{t} + d \frac{\partial θ_{2}}{∂t} & left = 0, \\ right n \frac{\partial θ_{2}}{∂t} - DΔ θ_{2} + γ_{2} \nabla^{T} U_{t} + d \frac{\partial θ_{1}}{∂t} & left = 0 . \end{matrix}

The treatment of those models is more delicate than in 1D. The interested reader can find results for thermoelasticity in 2D in and for 3D in by generalizing the approach we followed in this paper. In , one can find results for nonlinear 3D models of thermodiffusion in a micropolar medium in bounded domains. Remark There exist several proposals to model the thermal behavior in models of thermoelasticity.…”

Section: Some Concluding Remarksmentioning

confidence: 99%

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