Cahn-Hilliard-Brinkman systems for tumour growth
From MaRDI portal
Publication:2062938
DOI10.3934/dcdss.2021034zbMath1480.35411arXiv2003.08314OpenAlexW3011798359MaRDI QIDQ2062938
Matthias Ebenbeck, Robert Nürnberg, Harald Garcke
Publication date: 3 January 2022
Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.08314
existencefinite elementsphase field modelCahn-Hilliard equationtumour growthsingular limitBrinkman model
Initial-boundary value problems for higher-order parabolic equations (35K35) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Asymptotic expansions of solutions to PDEs (35C20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Free boundary problems for PDEs (35R35) Systems biology, networks (92C42)
Related Items (7)
Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms ⋮ Decoupled, linear, unconditionally energy stable and charge-conservative finite element method for an inductionless magnetohydrodynamic phase-field model ⋮ Viscoelastic Cahn–Hilliard models for tumor growth ⋮ From Vlasov equation to degenerate nonlocal Cahn-Hilliard equation ⋮ Existence analysis for a reaction-diffusion Cahn-Hilliard-type system with degenerate mobility and singular potential modeling biofilm growth ⋮ Incompressible limit for a two-species model with coupling through Brinkman's law in any dimension ⋮ Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- On a Cahn-Hilliard type phase field system related to tumor growth
- Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method
- Interactions between a uniformly proliferating tumour and its surroundings: stability analysis for variable material properties
- Finite element approximation of a three dimensional phase field model for void electromigration
- Second order phase field asymptotics for multi-component systems
- A free boundary problem for a coupled system of elliptic, hyperbolic, and Stokes equations modeling tumor growth
- Asymptotic behavior of solutions of a free boundary problem modelling the growth of tumors with Stokes equations
- Nonlinear simulation of tumor growth
- On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities
- On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms
- Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis
- Design of adaptive finite element software. The finite element toolbox ALBERTA. With CD-ROM
- Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
- Universal attractor for some singular phase transition systems
- Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance
- On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects
- A tractable mathematical model for tissue growth
- Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth
- Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching
- Well-posedness and long-time behavior of a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth
- An improved geometry-aware curvature discretization for level set methods: Application to tumor growth
- Method of Lagrange multipliers for exploitation of the entropy principle
- A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport
- Analysis of a mixture model of tumor growth
- THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES
- Numerical simulation of a thermodynamically consistent four-species tumor growth model
- Stable phase field approximations of anisotropic solidification
- Handbook of Mathematical Analysis in Mechanics of Viscous Fluids
- A Cahn-Hilliard-type equation with application to tumor growth dynamics
- Parametric finite element approximations of curvature-driven interface evolutions
- Mathematical Models of Avascular Tumor Growth
- Algorithm 849
- ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
- GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING
- Free Boundary Problems Associated with Multiscale Tumor Models
- Quasi–incompressible Cahn–Hilliard fluids and topological transitions
- Free boundary value problems associated with the growth and development of multicellular spheroids
- Interactions between a uniformly proliferating tumour and its surroundings: uniform material properties
- On a diffuse interface model of tumour growth
- A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis
- Finite Element Approximation of a Phase Field Model for Void Electromigration
- ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH
- On the Cahn–Hilliard Equation with Degenerate Mobility
- On the unsteady Darcy–Forchheimer–Brinkman equation in local and nonlocal tumor growth models
- Relaxation of the Cahn–Hilliard equation with singular single-well potential and degenerate mobility
- On a Cahn--Hilliard--Brinkman Model for Tumor Growth and Its Singular Limits
- Formal asymptotic limit of a diffuse-interface tumor-growth model
- MATHEMATICAL ANALYSIS AND CHALLENGES ARISING FROM MODELS OF TUMOR GROWTH
- Bifurcation for a Free Boundary Problem Modeling Tumor Growth by Stokes Equation
- Algorithm 832
- Algorithm 837
- Nonlinear modelling of cancer: bridging the gap between cells and tumours
- Mathematical Modeling
- Thermodynamics
This page was built for publication: Cahn-Hilliard-Brinkman systems for tumour growth
