Dissipativity of semilinear time fractional subdiffusion equations and numerical approximations

DOI10.1016/j.aml.2018.07.006zbMath1412.65134OpenAlexW2883538151WikidataQ129413129 ScholiaQ129413129MaRDI QIDQ1726472

Bianru Cheng, Dongling Wang, Zhen-Hua Guo

Publication date: 20 February 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2018.07.006

zbMATH Keywords

dissipativityabsorbing setfractional nonlinear sub-diffusion equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Fractional partial differential equations (35R11)

Related Items (11)

Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations ⋮ Long time behavior of Robin boundary sub-diffusion equation with fractional partial derivatives of Caputo type in differential and difference settings ⋮ High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation ⋮ Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations ⋮ Analytical and numerical dissipativity for the space-fractional Allen-Cahn equation ⋮ Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation ⋮ A novel discrete Gronwall inequality in the analysis of difference schemes for time-fractional multi-delayed diffusion equations ⋮ Blow-up and global solutions for a class of time fractional nonlinear reaction-diffusion equation with weakly spatial source ⋮ Polynomial stability of highly non-linear time-changed stochastic differential equations ⋮ Finite difference schemes for the two-dimensional multi-term time-fractional diffusion equations with variable coefficients ⋮ Semi-implicit Galerkin-Legendre spectral schemes for nonlinear time-space fractional diffusion-reaction equations with smooth and nonsmooth solutions

Cites Work

• Unnamed Item
• Unnamed Item
• A parabolic problem with a fractional time derivative
• Decay estimates for time-fractional and other non-local in time subdiffusion equations in \(\mathbb R^d\)
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• Dissipativity and contractivity for fractional-order systems
• Exponential attractors for reaction-diffusion equations with arbitrary polynomial growth
• Exponential attractors of reaction-diffusion systems in an unbounded domain
• Finite difference/spectral approximations for the time-fractional diffusion equation
• The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations
• A fully discrete difference scheme for a diffusion-wave system
• ASYMPTOTIC BEHAVIORS OF FUNDAMENTAL SOLUTION AND ITS DERIVATIVES TO FRACTIONAL DIFFUSION-WAVE EQUATIONS
• On the Stability of Linear Multistep Methods for Volterra Convolution Equations
• Well-posedness of the fractional Ginzburg–Landau equation
• Optimal Decay Estimates for Time-Fractional and Other NonLocal Subdiffusion Equations via Energy Methods

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