A Cahn--Hilliard Model for Cell Motility

DOI10.1137/19M1267969zbMath1452.35216OpenAlexW3062249572MaRDI QIDQ5124624

Alessandro Cucchi, Nicolas Meunier, Antoine Mellet

Publication date: 30 September 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1267969

zbMATH Keywords

Cahn-Hilliard equationsnonlinear fourth-order parabolic equationssharp interface limithysteresis phenomenaHele-Shaw free boundary problems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Degenerate parabolic equations (35K65) Free boundary problems for PDEs (35R35) Cell movement (chemotaxis, etc.) (92C17) Other free boundary flows; Hele-Shaw flows (76D27) Traveling wave solutions (35C07)

Related Items (4)

Self polarization and traveling wave in a model for cell crawling migration ⋮ \(\Gamma\) -Convergence of Some Nonlocal Perimeters in Bounded Domains with General Boundary Conditions ⋮ \(\Gamma\)-limit for a sharp interface model related to pattern formation on biomembranes ⋮ An isoperimetric problem with a competing nonlocal singular term

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Phase-field model of cell motility: traveling waves and sharp interface limit
• Global asymptotic limit of solutions of the Cahn-Hilliard equation
• The Hele--Shaw problem and area-preserving curve-shortening motions
• Higher order nonlinear degenerate parabolic equations
• A Gamma-convergence approach to the Cahn-Hilliard equation
• Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
• Sharp interface limit in a phase field model of cell motility
• Convergence of the Cahn-Hilliard equation to the Hele-Shaw model
• On an evolution equation in a cell motility model
• Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularization
• A DIFFUSE INTERFACE MODEL FOR ELECTROWETTING WITH MOVING CONTACT LINES
• Front migration in the nonlinear Cahn-Hilliard equation
• Classical Solutions of Multidimensional Hele--Shaw Models
• A Free Boundary Problem for an Elliptic-Hyperbolic System: An Application to Tumor Growth
• Gamma-convergence of gradient flows with applications to Ginzburg-Landau
• A diffuse interface approach to Hele Shaw flow
• A Free Boundary Problem for an Elliptic–Parabolic System: Application to a Model of Tumor Growth
• Global solutions for small data to the Hele-Shaw problem
• Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation

This page was built for publication: A Cahn--Hilliard Model for Cell Motility