Well-posedness for a fourth-order nonisothermal tumor growth model of Caginalp type
Abstract
We introduce a nonisothermal phase-field system of Caginalp type that describes tumor growth under hyperthermia. The model couples a possibly viscous Cahn-Hilliard equation, governing the evolution of the healthy and tumor phases, with an equation for the heat balance, and a reaction-diffusion equation for the nutrient concentration. The resulting nonlinear system incorporates chemotaxis and active transport effects, and is supplemented with no-flux boundary conditions. The analysis is carried out through a two-step approximation procedure, involving a regularization of the potential and a Faedo-Galerkin discretization scheme. Under stronger regularity assumptions, we further establish the existence of strong solutions and their uniqueness via a continuous dependence result.
Keywords
Cite
@article{arxiv.2508.07979,
title = {Well-posedness for a fourth-order nonisothermal tumor growth model of Caginalp type},
author = {Giulia Cavalleri and Pierluigi Colli and Elisabetta Rocca},
journal= {arXiv preprint arXiv:2508.07979},
year = {2025}
}
Comments
35 pages. The keywords are: nonlinear initial-boundary value problem, Cahn-Hilliard equation, nonisothermal model, well-posedness, regularity results, tumor growth