Existence, uniqueness, and time-asymptotics of regular solutions in multidimensional thermoelasticity on domains with boundary

Speaker(s)

Piotr Michał Bies

Affiliation

PW

Language of the talk

English

Date

April 23, 2026, 12:30 p.m.

Room

room 5070

Seminar

Seminar of Mathematical Physics Equations Group

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In the talk, we will discuss our results in nonlinear thermoelasticity.  We will study our issue in bounded and open domains. We will propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity. We will impose the Neumann boundary condition on the temperature. We will present the sketch of the proof of the existence of global, unique solutions for small initial data. We will also show that the temperature is bounded from below. Next, we will investigate the long-time behavior of solutions. We will show that the divergence-free part of the displacement oscillates.

On the other hand, we will present that the potential part and the temperature are strongly coupled. It will turn out that the non-rotation part tends to $0$ as $t$ approaches infinity. Additionally, the temperature will converge to a constant function.

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