Lipschitz stability for Bayesian inference in porous medium tissue growth models
Abstract
We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive relation between the pressure and cell density, the model can be written as a porous medium equation with a growth term. We prove Lipschitz continuity of the mild solutions of the model with respect to the diffusion parameter (the exponent in the pressure-density law) in the norm. While of independent analytical interest, our motivation for this result is to provide a vital step towards using Bayesian inverse problem methodology for parameter estimation based on experimental data -- such stability estimates are indispensable for applying sampling algorithms which rely on the gradient of the likelihood function.
Cite
@article{arxiv.2506.04769,
title = {Lipschitz stability for Bayesian inference in porous medium tissue growth models},
author = {Tomasz Dębiec and Piotr Gwiazda and Błażej Miasojedow and Katarzyna Ryszewska and Zuzanna Szymańska and Aneta Wróblewska-Kamińska},
journal= {arXiv preprint arXiv:2506.04769},
year = {2025}
}