A second-order numerical method for the aggregation equations
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Publication:5130997
DOI10.1090/mcom/3563zbMath1452.65186arXiv1804.07796OpenAlexW3041627545MaRDI QIDQ5130997
Susanne Solem, Ulrik Skre Fjordholm, José Antonio Carrillo
Publication date: 31 October 2020
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1804.07796
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Weak solutions to PDEs (35D30) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Integro-partial differential equations (35R09) PDEs with measure (35R06)
Uses Software
Cites Work
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- Equivalence between duality and gradient flow solutions for one-dimensional aggregation equations
- A nonlocal continuum model for biological aggregation
- Regularity of local minimizers of the interaction energy via obstacle problems
- One-dimensional aggregation equation after blow up: existence, uniqueness and numerical simulation
- Dimensionality of local minimizers of the interaction energy
- A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
- Stability of stationary states of non-local equations with singular interaction potentials
- Homogeneous cooling states are not always good approximations to granular flows
- Derivation of hyperbolic models for chemosensitive movement
- Contractions in the 2-Wasserstein length space and thermalization of granular media
- Initiation of slime mold aggregation viewed as an instability
- The Filippov characteristic flow for the aggregation equation with mildly singular potentials
- Diffusion and ecological problems: Modern perspectives.
- Convergence order of upwind type schemes for transport equations with discontinuous coefficients
- A parallel method for earth mover's distance
- An interacting particle system modelling aggregation behavior: from individuals to populations
- Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
- Long-time asymptotics of kinetic models of granular flows
- Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions
- On soccer balls and linearized inverse statistical mechanics
- Chemotaxis: from kinetic equations to aggregate dynamics
- Ring patterns and their bifurcations in a nonlocal model of biological swarms
- Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
- Nonlocal interactions by repulsive-attractive potentials: radial ins/stability
- Formation of clumps and patches in self-aggregation of finite-size particles
- Strong Stability-Preserving High-Order Time Discretization Methods
- Friction dominated dynamics of interacting particles locally close to a crystallographic lattice
- PREDICTING PATTERN FORMATION IN PARTICLE INTERACTIONS
- AGGREGATION AND SPREADING VIA THE NEWTONIAN POTENTIAL: THE DYNAMICS OF PATCH SOLUTIONS
- Heterophilious Dynamics Enhances Consensus
- Travelling plateaus for a hyperbolic Keller–Segel system with attraction and repulsion: existence and branching instabilities
- Numerical Simulation of Diffusive and Aggregation Phenomena in Nonlinear Continuity Equations by Evolving Diffeomorphisms
- Lp theory for the multidimensional aggregation equation
- STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS
- Swarm dynamics and equilibria for a nonlocal aggregation model
- Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
- One-dimensional transport equations with discontinuous coefficients
- Optimal L1-Rate of Convergence for The Viscosity Method and Monotone Scheme to Piecewise Constant Solutions with Shocks
- A kinetic equation for granular media
- Finite Volume Methods for Hyperbolic Problems
- Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
- Multilevel Optimal Transport: A Fast Approximation of Wasserstein-1 Distances
- Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D
- Numerical Methods for One-Dimensional Aggregation Equations
- Lagrangian Numerical Approximations to One‐Dimensional Convolution‐Diffusion Equations
- A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
- Self-Similar Blowup Solutions to an Aggregation Equation in $R^n$
- Second-Order Convergence of Monotone Schemes for Conservation Laws
