Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth

DOI10.4171/IFB/393zbMath1390.35431arXiv1610.04478MaRDI QIDQ1708578

Stefano Melchionna, Elisabetta Rocca

Publication date: 23 March 2018

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04478

zbMATH Keywords

tumor growthCahn-Hilliard equationDarcy lawfree boundary problemssharp interface limitdiffuse interface models

Mathematics Subject Classification ID

Variational inequalities (49J40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Free boundary problems for PDEs (35R35) General biology and biomathematics (92B05) Initial value problems for higher-order parabolic systems (35K46)

Related Items (12)

Analysis of a tumor model as a multicomponent deformable porous medium ⋮ On the long time behavior of a tumor growth model ⋮ Sharp interface limit of the Cahn–Hilliard reaction model for lithium-ion batteries ⋮ Sliding mode control for a phase field system related to tumor growth ⋮ Weak solutions of Mullins-Sekerka flow as a Hilbert space gradient flow ⋮ A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis ⋮ The Cahn-Hilliard-Hele-Shaw system with singular potential ⋮ Long-time dynamics and optimal control of a diffuse interface model for tumor growth ⋮ A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities ⋮ Well-posedness of a diffuse interface model for Hele-Shaw flows ⋮ On the Existence of Strong Solutions to the Cahn--Hilliard--Darcy System with Mass Source ⋮ Emergence of traveling waves and their stability in a free boundary model of cell motility

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