An Allen-Cahn tumor growth model with temperature

2025/10/15 by Stefania Gatti, Gatti, Stefania, Erica Ipocoana +3
Materials Science · #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2510.13283

Abstract

In this paper, we propose a new non-isothermal Allen-Cahn (Ginzburg-Landau) model for tumor growth. After deriving it using a microforces approach, we study its well-posedness. In particular, we are able to prove the existence and uniqueness of a local and global-in-time solution to our PDE system.

Citations

• Tumor evolution models of phase-field type with nonlocal effects and angiogenesis
• On a non-isothermal Cahn-Hilliard model for tumor growth
• Optimal control of cytotoxic and antiangiogenic therapies on prostate\n cancer growth
• On a non-isothermal Cahn-Hilliard model based on a microforce balance
• Mathematical analysis and simulation study of a phase-field model of\n prostate cancer growth with chemotherapy and antiangiogenic therapy effects
• On the long time behavior of a tumor growth model
• Regularity and long-time behavior for a thermodynamically consistent model for complex fluids in two space dimensions
• Existence of solutions to a two-dimensional model for nonisothermal\n two-phase flows of incompressible fluids
• Analysis of the Cahn-Hilliard equation with a chemical potential\n dependent mobility

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• Analysis of a mathematical model for tumor growth with Gibbs-Thomson relation
• On the hyperbolic relaxation of the chemical potential in a phase field tumor growth model