Vanishing viscosities and error estimate for a Cahn-Hilliard type phase field system related to tumor growth

DOI10.1016/j.nonrwa.2015.05.002zbMath1334.35097arXiv1501.07057OpenAlexW2606617955MaRDI QIDQ896464

Gianni Gilardi, Elisabetta Rocca, Pierluigi Colli, Juergen Sprekels

Publication date: 9 December 2015

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.07057

zbMATH Keywords

error estimatestumor growthCahn-Hilliard systemasymptotic analysisreaction-diffusion equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57) Medical applications (general) (92C50)

Related Items

A rigorous sharp interface limit of a diffuse interface model related to tumor growth ⋮ Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms ⋮ Optimal control of treatment time in a diffuse interface model of tumor growth ⋮ Analysis of a tumor model as a multicomponent deformable porous medium ⋮ Strong well-posedness and inverse identification problem of a non-local phase field tumour model with degenerate mobilities ⋮ Bounded solutions and their asymptotics for a doubly nonlinear Cahn-Hilliard system ⋮ Optimal control problems with sparsity for tumor growth models involving variational inequalities ⋮ Analysis of a diffuse interface model of multispecies tumor growth ⋮ On the long time behavior of a tumor growth model ⋮ Sliding mode control for a phase field system related to tumor growth ⋮ Well-posedness of a Cahn–Hilliard system modelling tumour growth with chemotaxis and active transport ⋮ Optimal control of an Allen-Cahn model for tumor growth through supply of cytotoxic drugs ⋮ Long-time dynamics for a Cahn-Hilliard tumor growth model with chemotaxis ⋮ Optimal distributed control for a viscous non-local tumour growth model ⋮ Optimal treatment for a phase field system of Cahn-Hilliard type modeling tumor growth by asymptotic scheme ⋮ Cahn–Hilliard–Brinkman model for tumor growth with possibly singular potentials ⋮ Optimal distributed control of an extended model of tumor growth with logarithmic potential ⋮ A structure-preserving upwind DG scheme for a degenerate phase-field tumor model ⋮ Second-Order Sufficient Conditions in the Sparse Optimal Control of a Phase Field Tumor Growth Model with Logarithmic Potential ⋮ Asymptotic analysis of a tumor growth model with fractional operators ⋮ Asymptotic analyses and error estimates for a Cahn-Hilliard type phase field system modelling tumor growth ⋮ Optimal distributed control of a Cahn-Hilliard-Darcy system with mass sources ⋮ Long-time dynamics and optimal control of a diffuse interface model for tumor growth ⋮ Penalisation of long treatment time and optimal control of a tumour growth model of Cahn-Hilliard type with singular potential ⋮ Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials ⋮ The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit ⋮ Second-order analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis ⋮ Optimality conditions for an extended tumor growth model with double obstacle potential via deep quench approach ⋮ A New Continuum Theory for Incompressible Swelling Materials ⋮ Inverse problem for a Cahn–Hilliard type system modeling tumor growth ⋮ On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport ⋮ Sparse optimal control of a phase field system with singular potentials arising in the modeling of tumor growth ⋮ Well-posedness and optimal control for a Cahn-Hilliard-Oono system with control in the mass term ⋮ Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth ⋮ The Cahn-Hilliard equation and some of its variants ⋮ On a Cahn-Hilliard-Keller-Segel model with generalized logistic source describing tumor growth ⋮ Parameter identification for nonlocal phase field models for tumor growth via optimal control and asymptotic analysis ⋮ On the Existence of Strong Solutions to the Cahn--Hilliard--Darcy System with Mass Source

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a Cahn-Hilliard type phase field system related to tumor growth
• On the Cahn-Hilliard equation
• Compact sets in the space \(L^ p(0,T;B)\)
• The viscous Cahn-Hilliard equation as a limit of the phase field model: Lower semicontinuity of the attractor
• Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis
• Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
• Viscous Cahn-Hilliard equation. II: Analysis
• Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching
• Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth
• Well-posedness of the Hele-Shaw-Cahn-Hilliard system
• On two classes of generalized viscous Cahn-Hilliard equations
• SELECTION AND ASSESSMENT OF PHENOMENOLOGICAL MODELS OF TUMOR GROWTH
• Numerical simulation of a thermodynamically consistent four-species tumor growth model
• GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING
• On a diffuse interface model of tumour growth
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Formal asymptotic limit of a diffuse-interface tumor-growth model
• Nonlinear Differential Equations of Monotone Types in Banach Spaces
• Nonlinear modelling of cancer: bridging the gap between cells and tumours