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Multidimensional Thermoelasticity for Nonsimple Materials -- Well-Posedness and Long-Time Behavior

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Andrii Anikushyn, Michael Pokojovy

Analysis of PDEs · Submitted 6 May 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim A Cattaneo-type hyperbolic relaxation for the thermal part is introduced and the well-posedness and uniform stability under a nonlinear frictional damping are obtained using a compactness-uniqueness-type argument.

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arXiv ID1605.02049 (version 1)
Pith ID2OEAHEDS, Pith's permanent record of this paper and its review
CitationAndrii Anikushyn, Michael Pokojovy. "Multidimensional Thermoelasticity for Nonsimple Materials -- Well-Posedness and Long-Time Behavior." arXiv:1605.02049 (2016). https://pith.science/paper/2OEAHEDS
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,341 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.59 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without Kelvin-Voigt and/or frictional damping in the elastic part as well as the lack of exponential stability in the elastically undamped case is proved. Further, a frictional damping for the elastic component is shown to lead to the exponential stability. A Cattaneo-type hyperbolic relaxation for the thermal part is introduced and the well-posedness and uniform stability under a nonlinear frictional damping are obtained using a compactness-uniqueness-type argument. Additionally, a connection between the exponential stability and exact observability for unitary $C_{0}$-groups is established.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. background 0.56 0.64 0.03 asserted 0.76
s1 In the linear case, the well-posedness with and without Kelvin-Voigt and/or frictional damping in the elastic part as well as the lack of exponential stability in the elastically undamped case is proved. result 0.97 0.91 0.19 asserted 1.00
s2 Further, a frictional damping for the elastic component is shown to lead to the exponential stability. result 0.99 0.90 0.20 asserted 1.00
s3 A Cattaneo-type hyperbolic relaxation for the thermal part is introduced and the well-posedness and uniform stability under a nonlinear frictional damping are obtained using a compactness-uniqueness-type argument. contribution 0.80 0.92 0.22 asserted 1.00
s4 Additionally, a connection between the exponential stability and exact observability for unitary $C_{0}$-groups is established. result 0.66 0.78 0.10 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without Kelvin-Voigt and/or frictional damping in the elastic part as well as the lack of exponential stability in the elastically undamped case is proved. Further, a frictional damping for the elastic component is shown to lead to the exponential stability. A Cattaneo-type hyperbolic relaxation for the thermal part is introduced and the well-posedness and uniform stability under a nonlinear frictional damping are obtained using a compactness-uniqueness-type argument. Additionally, a connection between the exponential stability and exact observability for unitary $C_{0}$-groups is established.

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