Tumor growth models with nutrient consumption
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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BibTeX
@misc{araujo2026tumor,
title = {{Tumor growth models with nutrient consumption}},
author = {Damião J. Araújo and Rafayel Teymurazyan and José Miguel Urbano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37144},
eprint = {2610.37144},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37144},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tumor growth models with nutrient consumption
AU - Damião J. Araújo
AU - Rafayel Teymurazyan
AU - José Miguel Urbano
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37144
UR - https://arxiv.org/abs/2610.37144
AB - 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.
ER -