Equivalence between duality and gradient flow solutions for one-dimensional aggregation equations
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Publication:256149
DOI10.3934/dcds.2016.36.1355zbMath1353.35109arXiv1303.5836OpenAlexW2219125663MaRDI QIDQ256149
François James, Nicolas Vauchelet
Publication date: 9 March 2016
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1303.5836
Optimality conditions for problems involving partial differential equations (49K20) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) First-order nonlinear hyperbolic equations (35L60) Weak solutions to PDEs (35D30)
Related Items (11)
Analysis and Simulation of Nonlinear and Nonlocal Transport Equations ⋮ Hydrodynamic singular regimes in \(1+1\) kinetic models and spectral numerical methods ⋮ One-dimensional aggregation equation after blow up: existence, uniqueness and numerical simulation ⋮ Convergence analysis of upwind type schemes for the aggregation equation with pointy potential ⋮ The Filippov characteristic flow for the aggregation equation with mildly singular potentials ⋮ A second-order numerical method for the aggregation equations ⋮ Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations ⋮ Synchronising and non-synchronising dynamics for a two-species aggregation model ⋮ Macroscopic Limits of Pathway-Based Kinetic Models for E. coli Chemotaxis in Large Gradient Environments ⋮ Numerical schemes for the aggregation equation with pointy potentials ⋮ Numerical Methods for One-Dimensional Aggregation Equations
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