1 citations · 1 across the 8 of their papers we have counts for
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Measure Differential Equation with a Nonlinear Growth/Decay Term
Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra +1
We obtain an existence result for a Measure Differential Equation with an additional nonlinear growth/decay term that may change the sign. The proof requires a modification of appr…
Dissipative measure-valued solutions to the Euler-Poisson equation
José A. Carrillo, Tomasz Dębiec, Piotr Gwiazda +1
We consider several pressureless variants of the compressible Euler equation driven by nonlocal repulsionattraction and alignment forces with Poisson interaction. Under an energy a…
Existence and differentiability in parameter of the measure solution to a perturbed non-linear transport equation
Piotr Gwiazda, Sander C. Hille, Kamila Łyczek
We consider a perturbation in the non-linear transport equation on measures i.e. both initial condition and the solution are bounded Radon measures $\mathcal{M}(\math…
On renormalized solutions to elliptic inclusions with nonstandard growth
Anna Denkowska, Piotr Gwiazda, Piotr Kalita
We study the elliptic inclusion given in the following divergence form \begin{align*} & -\mathrm{div}\, A(x,\nabla u) \ni f\quad \mathrm{in}\quad Ω, & u=0\quad \mathrm{on}\quad \pa…
Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws
Claude Bardos, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +2
We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fract…
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…