A random particle blob method for the Keller-Segel equation and convergence analysis

DOI10.1090/mcom/3118zbMath1355.60092OpenAlexW2400062562MaRDI QIDQ2953204

Rong Yang, Jian-Guo Liu

Publication date: 4 January 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/ef710c20c205b2fce012dfb3a50d55e24001ad77

zbMATH Keywords

chemotaxispropagation of chaosWasserstein distanceKeller-Segel equationNewtonian aggregationDobrushin-type stabilityinteracting Brownian particle systemmean-field nonlinear stochastic differential equationrandom particle blob method

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Applications of stochastic analysis (to PDEs, etc.) (60H30) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Stochastic particle methods (65C35) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items

Propagation of chaos for large Brownian particle system with Coulomb interaction ⋮ Primal dual methods for Wasserstein gradient flows ⋮ Propagation of chaos for the Keller-Segel equation over bounded domains ⋮ Propagation of Chaos for a Class of First Order Models with Singular Mean Field Interactions ⋮ Aggregation-Diffusion Equations: Dynamics, Asymptotics, and Singular Limits ⋮ Random batch methods (RBM) for interacting particle systems ⋮ A blob method for diffusion ⋮ Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation ⋮ Emergent behaviors of the swarmalator model for position-phase aggregation ⋮ Efficient numerical algorithms based on difference potentials for chemotaxis systems in 3D ⋮ Convergence of Diffusion-Drift Many Particle Systems in Probability Under a Sobolev Norm ⋮ Convergence of the Random Batch Method for Interacting Particles with Disparate Species and Weights ⋮ Error estimate of a random particle blob method for the Keller-Segel equation

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