4 papers
Existence, uniqueness, and time-asymptotics of regular solutions in multidimensional thermoelasticity on domains with boundary
Piotr MichaÅ Bies
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement.…
Existence, uniqueness, and long-time asymptotic behavior of regular solutions in multidimensional thermoelasticity
Piotr MichaÅ Bies, Tomasz CieÅlak, Mario Fuest +3
We study a simplified nonlinear thermoelasticity model on two- and three-dimensional tori. A novel functional involving the Fisher information associated with temperature is introd…
Decay of solutions of non-homogenous hyperbolic equations
Piotr MichaÅ Bies
We consider conditions for the decay in time of solutions of non-homogenous hyperbolic equations. It is proven that solutions of the equations go to in at infinity if and…
Time-asymptotics of a heated string
Piotr MichaÅ Bies, Tomasz CieÅlak
In the present paper, we study a model of a thermoelastic string that is initially heated. We classify all the possible asymptotic states when time tends to infinity of such a mode…