Analytical and numerical dissipativity for the space-fractional Allen-Cahn equation

DOI10.1016/j.matcom.2022.12.012OpenAlexW4313443050MaRDI QIDQ6102926

Unnamed Author, Wan-Sheng Wang

Publication date: 26 June 2023

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2022.12.012

zbMATH Keywords

dissipativityglobal attractorbackward Euler methodfractional Laplacian operatorspace-fractional Allen-Cahn equation

Mathematics Subject Classification ID

Dynamical systems and ergodic theory (37-XX) Partial differential equations (35-XX)

Cites Work

• Unnamed Item
• Unnamed Item
• Hitchhiker's guide to the fractional Sobolev spaces
• Fourier spectral methods for fractional-in-space reaction-diffusion equations
• Analytical and numerical dissipativity for nonlinear generalized pantograph equations
• Invariant measures for dissipative dynamical systems: abstract results and applications
• The spectral collocation method for efficiently solving PDEs with fractional Laplacian
• Generalized Halanay inequalities for dissipativity of Volterra functional differential equations
• Dissipativity of Runge-Kutta methods for neutral delay differential equations with piecewise constant delay
• Integral manifolds and inertial manifolds for dissipative partial differential equations
• Infinite-dimensional dynamical systems in mechanics and physics.
• Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation
• Optimal error estimate of the Legendre spectral approximation for space-fractional reaction-advection-diffusion equation
• Dissipativity of semilinear time fractional subdiffusion equations and numerical approximations
• Convergence of exponential attractors for a time semi-discrete reaction-diffusion equation
• A fractional diffusion equation to describe Lévy flights
• Stable second-order schemes for the space-fractional Cahn-Hilliard and Allen-Cahn equations
• On diagonal dominance of FEM stiffness matrix of fractional Laplacian and maximum principle preserving schemes for the fractional Allen-Cahn equation
• Long time \(\mathcal{H}_\alpha^s\) stability of a classical scheme for Cahn-Hilliard equation with polynomial nonlinearity
• A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
• What is the fractional Laplacian? A comparative review with new results
• 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
• Local discontinuous Galerkin scheme for space fractional Allen-Cahn equation
• A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation
• Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations
• A fractional phase-field model for two-phase flows with tunable sharpness: algorithms and simulations
• Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations
• An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
• Fractional Partial Differential Equations and Their Numerical Solutions
• Approximation of stationary statistical properties of dissipative dynamical systems: Time discretization
• Phase-Field Models for Multi-Component Fluid Flows
• Dissipativity of the linearly implicit Euler scheme for Navier‐Stokes equations with delay
• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
• Analysis and Approximation of a Fractional Cahn--Hilliard Equation
• An Energy Stable and Maximum Bound Preserving Scheme with Variable Time Steps for Time Fractional Allen--Cahn Equation
• Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights
• Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations
• Dynamics of evolutionary equations

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