Tumor growth models with nutrient consumption

Damião J. Araújo; Rafayel Teymurazyan; José Miguel Urbano

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arXiv · 2610.37144

Tumor growth models with nutrient consumption

Damião J. Araújo·Rafayel Teymurazyan·José Miguel Urbano

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Abstract

We study the saturation free boundary of the cell density and its interaction with the nutrient depletion interface in a coupled parabolic model for tumor growth with sublinear reactions. We establish a sharp quadratic--superquadratic growth dichotomy along the saturation interface and quantify the degeneration of quadratic profiles as they approach the joint saturation--depletion boundary. We further show that intrinsic regularity of the saturation interface can occur only at joint free boundary points, where half-space blow-ups of either component determine a unique joint blow-up profile. Finally, we prove a local backward coincidence between the joint and nutrient free boundaries near regular points, which yields spatial and temporal regularity of the joint interface.

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Damião J. Araújo, Rafayel Teymurazyan, José Miguel Urbano. 2026-10-27. Tumor growth models with nutrient consumption. https://arxiv.org/abs/2610.37144

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