A fitness-driven cross-diffusion system from population dynamics as a gradient flow

DOI10.1016/j.jde.2016.05.012zbMath1343.35132arXiv1603.06431OpenAlexW2963666342MaRDI QIDQ294216

F. Blanchet-Sadri, M. Dambrine

Publication date: 9 June 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.06431

zbMATH Keywords

gradient flowcross-diffusionoptimal transportideal free distributionentropy-entropy production inequality

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Variational problems in a geometric measure-theoretic setting (49Q20) Degenerate parabolic equations (35K65) Ecology (92D40) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (13)

A new transportation distance with bulk/interface interactions and flux penalization ⋮ On geodesic completeness for Riemannian metrics on smooth probability densities ⋮ On cross-diffusion systems for two populations subject to a common congestion effect ⋮ An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems ⋮ A non-local cross-diffusion model of population dynamics I: emergent spatial and spatiotemporal patterns ⋮ A transportation \(L^p\) distance for signal analysis ⋮ Strong solutions and instability for the fitness gradient system in evolutionary games between two populations ⋮ Modeling of invasion on a heterogeneous habitat: taxis and multistability ⋮ A new multicomponent Poincaré-Beckner inequality ⋮ Nonlinear Fokker-Planck equations with reaction as gradient flows of the free energy ⋮ Convex Sobolev inequalities related to unbalanced optimal transport ⋮ A minimizing Movement approach to a class of scalar reaction–diffusion equations ⋮ A tumor growth model of Hele-Shaw type as a gradient flow

Cites Work

• Qualitative behavior of solutions to cross-diffusion systems from population dynamics
• Well-posedness and qualitative properties of a dynamical model for the ideal free distribution
• A new multicomponent Poincaré-Beckner inequality
• Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
• Approximating the ideal free distribution via reaction-diffusion-advection equations
• Stability of a 4th-order curvature condition arising in optimal transport theory
• Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
• Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion
• A new optimal transport distance on the space of finite Radon measures
• Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures
• An interpolating distance between optimal transport and Fisher-Rao metrics
• Diffusion, self-diffusion and cross-diffusion
• Random dispersal versus fitness-dependent dispersal
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Weak solvability for equations of viscoelastic diffusion in polymers with variable coefficients
• Analysis of a parabolic cross-diffusion population model without self-diffusion
• A dynamic model for the ideal-free distribution as a partial differential equation
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves
• Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates
• Topological Approximation Methods for Evolutionary Problems of Nonlinear Hydrodynamics
• A Family of Nonlinear Fourth Order Equations of Gradient Flow Type
• Beyond Diffusion: Conditional Dispersal in Ecological Models
• The boundedness-by-entropy method for cross-diffusion systems
• Existence result for degenerate cross-diffusion system with application to seawater intrusion
• Approaching the Ideal Free Distribution in Two-Species Competition Models with Fitness-Dependent Dispersal
• A JKO Splitting Scheme for Kantorovich--Fisher--Rao Gradient Flows
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