On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion

DOI10.1016/j.na.2017.03.010zbMath1366.35064arXiv1609.05024OpenAlexW2963905938MaRDI QIDQ2361689

Jan-Frederik Pietschmann, Martin Burger, Judith Berendsen

Publication date: 30 June 2017

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.05024

zbMATH Keywords

cross-diffusionnonlocal interactionsize exclusion

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Degenerate parabolic equations (35K65) Theoretical approximation in context of PDEs (35A35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Continuation and prolongation of solutions to PDEs (35B60) Second-order parabolic systems (35K40)

Related Items (17)

Nonlocal cross-diffusion systems for multi-species populations and networks ⋮ Mean-field models for segregation dynamics ⋮ On nonlinear cross-diffusion systems: an optimal transport approach ⋮ On multi-species diffusion with size exclusion ⋮ Nonlocal Cross-Interaction Systems on Graphs: Nonquadratic Finslerian Structure and Nonlinear Mobilities ⋮ Nonlocal cross-interaction systems on graphs: energy landscape and dynamics ⋮ Exponential Convergence to Equilibrium for Coupled Systems of Nonlinear Degenerate Drift Diffusion Equations ⋮ Equilibria for an Aggregation Model with Two Species ⋮ A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model ⋮ Existence of weak solutions to a cross-diffusion Cahn-Hilliard type system ⋮ On a Reaction-Cross-Diffusion System Modeling the Growth of Glioblastoma ⋮ Convergence and non-convergence of many-particle evolutions with multiple signs ⋮ Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise ⋮ On a terminal value problem for parabolic reaction-diffusion systems with nonlocal coupled diffusivity terms ⋮ Convergence of a finite volume scheme for a system of interacting species with cross-diffusion ⋮ The continuum limit of interacting dislocations on multiple slip systems ⋮ Macroscopic behaviour in a two-species exclusion process via the method of matched asymptotics

Cites Work

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• Regularity of local minimizers of the interaction energy via obstacle problems
• Stationary states of quadratic diffusion equations with long-range attraction
• Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion
• Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
• On an evolution system describing self-gravitating particles in microcanonical setting
• Global minimizers for free energies of subcritical aggregation equations with degenerate diffusion
• Compact families of piecewise constant functions in \(L^p (0,T;B)\)
• Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis
• Volume effects in the Keller--Segel model: energy estimates preventing blow-up
• On minimizers of interaction functionals with competing attractive and repulsive potentials
• Minimal interface criterion for phase transitions in mixtures of Cahn- Hilliard fluids
• Large time behavior of nonlocal aggregation models with nonlinear diffusion
• A user's guide to PDE models for chemotaxis
• Numerical simulations of immiscible fluid clusters
• A non-local model for a swarm
• Modeling the aggregative behavior of ants of the species Polyergus rufescens
• On anisotropic order parameter models for multi-phase systems and their sharp interface limits
• Uniqueness of strong solutions and weak-strong stability in a system of cross-diffusion equations
• Global existence analysis for degenerate energy-transport models for semiconductors
• Existence of ground states of nonlocal-interaction energies
• Existence of compactly supported global minimisers for the interaction energy
• Nonlocal interactions by repulsive-attractive potentials: radial ins/stability
• On an aggregation model with long and short range interactions
• Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions
• Multiplier and gradient methods
• On fully practical finite element approximations of degenerate Cahn-Hilliard systems
• Lane Formation by Side-Stepping
• Splitting Methods in Communication, Imaging, Science, and Engineering
• An Aggregation Equation with Degenerate Diffusion: Qualitative Property of Solutions
• Stationary States and Asymptotic Behavior of Aggregation Models with Nonlinear Local Repulsion
• Nonlinear Poisson–Nernst–Planck equations for ion flux through confined geometries
• Stationary States of an Aggregation Equation with Degenerate Diffusion and Bounded Attractive Potential
• Existence and Asymptotic Properties of Solutions of a Nonlocal Evolution Equation Modeling Cell-Cell Adhesion
• Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion
• Lp theory for the multidimensional aggregation equation
• STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS
• Optimization with PDE Constraints
• Coarsening in Nonlocal Interfacial Systems
• A multi-phase Mullins–Sekerka system: matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem
• Nonlinear Cross-Diffusion with Size Exclusion
• The boundedness-by-entropy method for cross-diffusion systems
• The Keller–Segel Model for Chemotaxis with Prevention of Overcrowding: Linear vs. Nonlinear Diffusion
• The Keller--Segel Model with Logistic Sensitivity Function and Small Diffusivity
• Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix
• A singular limit for a system of degenerate Cahn-Hilliard equations
• Transport distances and geodesic convexity for systems of degenerate diffusion equations

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