Shows convergence to weak solutions in tissue growth modeling, suggesting effective modeling techniques.
We study a porous medium equation that models tissue growth in a heterogeneous environment. We show that, in the incompressible limit, solutions converge to those of a weak form of a Hele-Shaw type free boundary problem. To obtain enough compactness to take the limit, we establish an L⁴ L 4 bound on the gradient of the pressure and an estimate of Aronson-Bénilan type.
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Sulak et al. (2026) studied this question.
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