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arXiv · 2506.04769

Lipschitz stability for Bayesian inference in porous medium tissue growth models

Tomasz Dębiec·Piotr Gwiazda·Błażej Miasojedow·Katarzyna Ryszewska·Zuzanna Szymańska·Aneta Wróblewska-Kamińska
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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 $\gamma$ in the pressure-density law) in the $L_1$ 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.

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Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow, Katarzyna Ryszewska, Zuzanna Szymańska, Aneta Wróblewska-Kamińska. 2025-06-05. Lipschitz stability for Bayesian inference in porous medium tissue growth models. https://arxiv.org/abs/2506.04769

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