1 citations · 1 across the 10 of their papers we have counts for
10 papers
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…
Beyond Bayesian Inference: The Correlation Integral Likelihood Framework and Gradient Flow Methods for Deterministic Sampling
Piotr Gwiazda, Alexey Kazarnikov, Anna Marciniak-Czochra +1
Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due t…
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…
Operator splitting algorithm for structured population models on metric spaces
Carolin Lindow, Christian Düll, Piotr Gwiazda +2
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of…
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…
Structured Population Models on Polish spaces: A unified Approach including Graphs, Riemannian Manifolds and Measure Spaces to describe Dynamics of Heterogeneous Populations
Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra +1
This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes, dependent…
The Escalator Boxcar Train Method for a System of Aged-structured Equations in the Space of Measures
José A. Carrillo, Piotr Gwiazda, Karolina Kropielnicka +1
The Escalator Boxcar Train (EBT) method is a well known and widely used numerical method for one-dimensional structured population models of McKendrick-von Foerster type. Recently…