Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions

DOI10.1007/978-3-030-43651-3_20zbMath1454.65086arXiv1912.06423OpenAlexW3044572032MaRDI QIDQ5117442

Anissa El Keurti, Thomas Rey

Publication date: 25 August 2020

Published in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.06423

zbMATH Keywords

population dynamicsmeasure-valued solutionscontinuity equationsupwind finite volume methodsystem of aggregation equations

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Input-output approaches in control theory (93D25) Stability and convergence of numerical methods for ordinary differential equations (65L20) Computational methods for problems pertaining to biology (92-08) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Integro-partial differential equations (35R09) PDEs with measure (35R06)

Related Items (1)

Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation

Cites Work

• The Filippov characteristic flow for the aggregation equation with mildly singular potentials
• Convergence order of upwind type schemes for transport equations with discontinuous coefficients
• Measure solutions to a system of continuity equations driven by Newtonian nonlocal interactions
• A nonlocal swarm model for predators–prey interactions
• Measure solutions for non-local interaction PDEs with two species
• Blow-up in multidimensional aggregation equations with mildly singular interaction kernels

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