3 citations · 3 across the 7 of their papers we have counts for
9 papers
Existence, uniqueness, and time-asymptotics of regular solutions in multidimensional thermoelasticity on domains with boundary
Piotr Michał 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 Michał Bies, Tomasz Cieślak, 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 Michał 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 Michał Bies, Tomasz Cieślak
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…
Maximal operator in Musielak--Orlicz--Sobolev spaces
Piotr Michał Bies, Michał Gaczkowski, Przemysław Górka
We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev space . Under some natural assumptions on we show that the maximal function…
Maximal operator in Hölder spaces
Piotr Michał Bies, Michał Gaczkowski, Przemysław Górka
We study the maximal operator on the variable exponent Hölder spaces in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annu…
Global-in-time regular unique solutions with positive temperature to the 1d thermoelasticity
Piotr Michał Bies, Tomasz Cieślak
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 esti…
A priori estimates and theory of existence for parabolic equations in variable Hölder spaces
Piotr Michał Bies
We study parabolic equations in variable Hölder spaces on domains of Euclidean spaces. The existence and uniqueness of solutions is proved.
Schauder theory in variable Hölder spaces
Piotr Michał Bies, Przemysław Górka
We study elliptic equations on bounded domain of Euclidean spaces in the variable Hölder spaces. Interior a priori Schauder estimates are given as well as global ones. Moreover, th…