Long-time behavior of non-local in time Fokker–Planck equations via the entropy method

DOI10.1142/S0218202519500076zbMath1411.35272arXiv1708.04572OpenAlexW2964280407WikidataQ128780922 ScholiaQ128780922MaRDI QIDQ4630573

Rico Zacher, Jukka T. Kemppainen

Publication date: 27 March 2019

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.04572

zbMATH Keywords

entropy methodfractional derivativesubdiffusiontime-discrete schemetemporal decay estimatesnon-local Fokker-Planck equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Integro-partial differential equations (45K05) Integro-differential operators (47G20) Fractional partial differential equations (35R11) Fokker-Planck equations (35Q84)

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Cites Work

• Unnamed Item
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• Decay estimates for time-fractional and other non-local in time subdiffusion equations in \(\mathbb R^d\)
• Representation of solutions and large-time behavior for fully nonlocal diffusion equations
• Maximal regularity of type \(L_p\) for abstract parabolic Volterra equations
• Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients
• Entropy decay of discretized Fokker-Planck equations. I: Temporal semidiscretization
• A De Giorgi-Nash type theorem for time fractional diffusion equations
• Fractional Cauchy problems on bounded domains
• SDEs driven by a time-changed Lévy process and their associated time-fractional order pseudo-differential equations
• Distributed order calculus and equations of ultraslow diffusion
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• Entropy Methods for Diffusive Partial Differential Equations
• Asymptotic Behavior of Solutions of Nonlinear Volterra Equations with Completely Positive Kernels
• The Variational Formulation of the Fokker--Planck Equation
• Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Discrete versions of the Li-Yau gradient estimate
• Stochastic Processes and Applications
• Weak Solutions of Abstract Evolutionary Integro-Differential Equations in Hilbert Spaces
• Optimal Decay Estimates for Time-Fractional and Other NonLocal Subdiffusion Equations via Energy Methods
• The random walk's guide to anomalous diffusion: A fractional dynamics approach