Global-in-time regular unique solutions with positive temperature to the 1d thermoelasticity

Piotr Michał Bies; Tomasz Cieślak

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arXiv · 2303.12522

Global-in-time regular unique solutions with positive temperature to the 1d thermoelasticity

Piotr Michał Bies·Tomasz Cieślak

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Abstract

We construct unique regular solutions to the minimal nonlinear system of the 1d thermoelasticity. The obtained solution has a positive temperature. Our approach is based on an estimate, using the Fisher information, which seems completely new in this context. It is combined with a recent inequality in [2] and embeddings, which allows us to obtain a new energy estimate. The latter is used in a half-Galerkin procedure yielding global solutions. The uniqueness and further regularity of such solutions are obtained.

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Piotr Michał Bies, Tomasz Cieślak. 2023-03-22. Global-in-time regular unique solutions with positive temperature to the 1d thermoelasticity. https://arxiv.org/abs/2303.12522

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