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

Prelegent(ci)

Piotr Michał Bies

Afiliacja

PW

Język referatu

angielski

Termin

23 kwietnia 2026 12:30

Pokój

p. 5070

Seminarium

Seminarium Zakładu Równań Fizyki Matematycznej

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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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