96 citations · 217 across the 23 of their papers we have counts for
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Conservation of energy for the Euler-Korteweg equations
Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +1
In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the…
Relative entropy method for measure-valued solutions in natural sciences
Tomasz Dębiec, Piotr Gwiazda, Kamila Łyczek +1
In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the n…
A tribute to conservation of energy for weak solutions
Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolu…
Existence of global weak solutions to the kinetic Peterlin model
Piotr Gwiazda, Mária Lukáčová-Medviďová, Hana Mizerová +1
We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely ex…
A note on weak solutions of conservation laws and energy/entropy conservation
Piotr Gwiazda, Martin Michálek, Agnieszka Świerczewska-Gwiazda
A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such case most often related to the second l…
Homogenization of nonlinear elliptic systems in nonreflexive Musielak-Orlicz spaces
Miroslav Bulíček, Piotr Gwiazda, Martin Kalousek +1
We study the homogenization process for families of strongly nonlinear elliptic systems with the homogeneous Dirichlet boundary conditions. The growth and the coercivity of the ell…