Stability of solutions of the porous medium equation with growth with respect to the diffusion exponent
CoRR(2024)
Abstract
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 the mechanical pressure and the cell
density, the model can be expressed as the porous medium equation with a growth
term. We prove Hölder continuous dependence of the solutions of the model on
the diffusion exponent. The main difficulty lies in the degeneracy of the
porous medium equations at vacuum. To deal with this issue, we first regularise
the equation by shifting the initial data away from zero and then optimise the
stability estimate derived in the regular setting.
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