Cahn-Hilliard models for glial cells

DOI10.1007/s00245-020-09696-xzbMath1475.35176OpenAlexW3037516758MaRDI QIDQ2232778

Lu Li, Alain Miranville, Rémy Guillevin

Publication date: 8 October 2021

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00245-020-09696-x

zbMATH Keywords

regularityexistenceCahn-Hilliard equationlogarithmic nonlinear termstrict separationCahn-Hilliard-Oono equationsymport term

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) A priori estimates in context of PDEs (35B45) Semilinear parabolic equations (35K58)

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Cites Work

• Unnamed Item
• Unnamed Item
• A mathematical model for the glucose-lactate metabolism of in vitro cancer cells
• A generalized diffusion model for growth and dispersal in a population
• Infinite-dimensional dynamical systems in mechanics and physics.
• Existence and uniqueness of weak solutions for a class of fractional superdiffusion equations
• Analysis of a mathematical model for brain lactate kinetics
• Area-preserving curve-shortening flows: From phase separation to image processing
• Analysis of a mathematical model for the glutamate/glutamine cycle in the brain
• Mathematical modeling of brain metabolites variations in the circadian rhythm
• Mathematical analysis of a model for proliferative-to-invasive transition of hypoxic glioma cells
• On the long time behavior of a tumor growth model
• Mathematical physiology. I: Cellular physiology
• A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport
• Adaptive, second-order in time, primitive-variable discontinuous Galerkin schemes for a Cahn–Hilliard equation with a mass source
• A singular reaction‐diffusion equation associated with brain lactate kinetics
• Inpainting of Binary Images Using the Cahn–Hilliard Equation
• Convergence of solutions to cahn-hilliard equation
• Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials
• The Cahn–Hilliard–Oono equation with singular potential
• A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis
• The Cahn–Hilliard Equation: Recent Advances and Applications
• Free Energy of a Nonuniform System. I. Interfacial Free Energy