Front-type solutions of fractional Allen-Cahn equation

DOI10.1016/j.physd.2008.08.002zbMath1160.35442OpenAlexW2087982179MaRDI QIDQ1000762

A. A. Golovin, Alexander A. Nepomnyashchy, Yana Nec

Publication date: 10 February 2009

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2008.08.002

zbMATH Keywords

fractional Allen-Cahn equationdomain wall dynamicsanomalous front

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) PDEs in connection with fluid mechanics (35Q35) Reaction-diffusion equations (35K57) Fractional derivatives and integrals (26A33) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (26)

Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations ⋮ V-shaped traveling fronts of fractional Allen–Cahn equations ⋮ Domain coarsening in a subdiffusive Allen-Cahn equation ⋮ On the speed of spread for fractional reaction-diffusion equations ⋮ A fractional phase-field model for two-phase flows with tunable sharpness: algorithms and simulations ⋮ A Quadrature Scheme for Steady-State Diffusion Equations Involving Fractional Power of Regularly Accretive Operator ⋮ Fronts in anomalous diffusion–reaction systems ⋮ Finite element simulation and efficient algorithm for fractional Cahn-Hilliard equation ⋮ Second-order linear adaptive time-stepping schemes for the fractional Allen-Cahn equation ⋮ On the limit of solutions for a reaction-diffusion equation containing fractional Laplacians ⋮ An adaptive unconditional maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation ⋮ A new linearized maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation ⋮ The stability of the equilibria of the Allen–Cahn equation with fractional diffusion ⋮ Traveling wave solutions of Allen-Cahn equation with a fractional Laplacian ⋮ On the preserving of the maximum principle and energy stability of high-order implicit-explicit Runge-Kutta schemes for the space-fractional Allen-Cahn equation ⋮ Metastable speeds in the fractional Allen-Cahn equation ⋮ Exact solutions in front propagation problems with superdiffusion ⋮ On Energy Dissipation Theory and Numerical Stability for Time-Fractional Phase-Field Equations ⋮ Image segmentation based on modified fractional Allen-Cahn equation ⋮ Efficient implementation and numerical analysis of finite element method for fractional Allen-Cahn equation ⋮ A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation ⋮ A Schwarz waveform relaxation method for time-dependent space fractional Schrödinger/heat equations ⋮ Propagation acceleration in reaction diffusion equations with anomalous diffusions ⋮ The stability of traveling waves for Allen–Cahn equations with fractional Laplacian ⋮ Cahn-Hilliard equation with nonlocal singular free energies ⋮ Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions

Cites Work

• Finite difference approximations for fractional advection-dispersion flow equations
• Estimates and structure of \(\alpha\)-harmonic functions
• Patterns and interfaces in dissipative dynamics. With a foreword by Y. Pomeau
• Anomalous behaviour of a passive tracer in wave turbulence
• Non-equilibrium phase transitions with long-range interactions
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
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