7 papers · 1 filter
A note on application of mean-field limit to non-exchangeable non-conservative systems
Piotr Gwiazda, Katarzyna Ryszewska
In this paper we apply the newly developed theory of extended graphons to a certain class of non-exchangeable, non-conservative problems. We establish the mean-field limit by provi…
Asynchronous exponential growth for structured population models in measure space
Christian Düll, József Z. Farkas, Piotr Gwiazda +1
This paper studies the asymptotic behaviour of a structured population model on the space of nonnegative Radon measures. Such formulations naturally arise when solutions develop co…
Stochastic parabolic equations in Musielak-Orlicz spaces with discontinuous in time N-function
Piotr Gwiazda, Jakub Woźnicki, Aneta Wróblewska-Kamińska +1
We consider a stochastic parabolic partial differential equation with Dirichlet boundary conditions, multiplicative stochastic noise, and a monotone parabolic operator A. The growt…
Lipschitz stability for Bayesian inference in porous medium tissue growth models
Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow +3
We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive rela…
Rigorous derivation of magneto-Oberbeck-Boussinesq approximation with non-local temperature term
Piotr Gwiazda, Florian Oschmann, Aneta Wróblewska-Kamińska
We consider a general compressible, viscous, heat and magnetically conducting fluid described by the compressible Navier-Stokes-Fourier system coupled with induction equation. In p…
Stability of solutions of the porous medium equation with growth with respect to the diffusion exponent
Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow +1
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between…