On the effects of a wide opening in the domain of the (stochastic) Allen-Cahn equation and the motion of hybrid zones

DOI10.1214/22-EJP888MaRDI QIDQ2679551

Ian Letter, Alison M. Etheridge, Mitchel D. Gooding

Publication date: 23 January 2023

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.00316

zbMATH Keywords

mean curvature flowpopulation geneticsreflecting boundary conditionsgenetic driftbranching Brownian motionhybrid zonesspatial \(\Lambda\)-Fleming-Viot

Mathematics Subject Classification ID

Problems related to evolution (92D15) Applications of branching processes (60J85) Applications of stochastic analysis (to PDEs, etc.) (60H30) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (1)

Branching stable processes and motion by mean curvature flow

Cites Work

• Unnamed Item
• Triviality of the 2D stochastic Allen-Cahn equation
• Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
• The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system
• Reaction-diffusion equations for interacting particle systems
• Generation and propagation of interfaces for reaction-diffusion equations
• Branching Brownian motion and selection in the spatial \(\Lambda\)-Fleming-Viot process
• Branching Brownian motion, mean curvature flow and the motion of hybrid zones
• Singular limit for stochastic reaction-diffusion equation and generation of random interfaces
• The scaling limit for a stochastic PDE and the separation of phases
• The spatial \(\Lambda\)-Fleming-Viot process on a large torus: genealogies in the presence of recombination
• Rescaling limits of the spatial Lambda-Fleming-Viot process with selection
• The spatial lambda-Fleming-Viot process: an event-based construction and a lookdown representation
• Front blocking and propagation in cylinders with varying cross section
• Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov
• Generation of interfaces for multi-dimensional stochastic Allen–Cahn equation with a noise smooth in space
• Branching Diffusion Processes
• Existence and Nonexistence of Traveling Wave Solutions for a Bistable Reaction-Diffusion Equation in an Infinite Cylinder Whose Diameter is Suddenly Increased

This page was built for publication: On the effects of a wide opening in the domain of the (stochastic) Allen-Cahn equation and the motion of hybrid zones