96 citations · 490 across the 38 of their papers we have counts for
8 papers · 1 filter
A two species hyperbolic-parabolic model of tissue growth
Piotr Gwiazda, Benoît Perthame, Agnieszka Świerczewska-Gwiazda
Models of tissue growth are now well established, in particular in relation to their applications to cancer. They describe the dynamics of cells subject to motion resulting from a…
Renormalized solutions to parabolic equations in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon
Iwona Chlebicka, Piotr Gwiazda, Anna Zatorska-Goldstein
We provide existence and uniqueness of renomalized solutions to a general nonlinear parabolic equation with merely integrable data on a Lipschitz bounded domain in .…
Parabolic equation in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon
Iwona Chlebicka, Piotr Gwiazda, Anna Zatorska-Goldstein
We study a general nonlinear parabolic equation on a Lipschitz bounded domain in , \begin{equation*} \left\{\begin{array}{l l} \partial_t u-\mathrm{div} A(t,x,\nabla…
On the Extension of Onsager's Conjecture for General Conservation Laws
Claude Bardos, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +2
The aim of this work is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the "…
Differentiability in perturbation parameter of measure solutions to perturbed transport equation
Piotr Gwiazda, Sander C. Hille, Kamila Łyczek +1
We consider a linear perturbation in the velocity field of the transport equation. We investigate solutions in the space of bounded Radon measures and show that they are differenti…
Relative Entropy Method for Measure Solutions of the Growth-Fragmentation Equation
Tomasz Dębiec, Marie Doumic, Piotr Gwiazda +1
The aim of this study is to generalise recent results of the two last authors on en-tropy methods for measure solutions of the renewal equation to other classes of structured popul…
Existence and homogenization of nonlinear elliptic systems in nonreflexive spaces
Miroslav Bulíček, Piotr Gwiazda, Martin Kalousek +1
We consider a strongly nonlinear elliptic problem with the homogeneous Dirichlet boundary condition. The growth and the coercivity of the elliptic operator is assumed to be indicat…
Dissipative measure valued solutions for general conservation laws
Piotr Gwiazda, Ondřej Kreml, Agnieszka Świerczewska-Gwiazda
In the last years measure-valued solutions started to be considered as a relevant notion of solutions if they satisfy the so-called measure-valued -- strong uniqueness principle. T…