Fractional Fokker--Planck Equation with General Confinement Force
DOI10.1137/18M1188331zbMath1435.35386arXiv1803.02672OpenAlexW2789548416MaRDI QIDQ5208769
Publication date: 10 January 2020
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1803.02672
asymptotic behaviorfractional LaplacianFokker-Planckfractional diffusion with driftconfinement force
Asymptotic behavior of solutions to PDEs (35B40) Integro-partial differential equations (45K05) One-parameter semigroups and linear evolution equations (47D06) Estimates of eigenvalues in context of PDEs (35P15) Functional-differential equations in abstract spaces (34K30) Asymptotics of solutions to integral equations (45M05) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Linear differential equations in abstract spaces (34G10) Eigenvalue problems for integral equations (45C05) Integro-differential operators (47G20) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09) Fokker-Planck equations (35Q84)
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Cites Work
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- Spectral analysis of semigroups and growth-fragmentation equations
- Exponential stability of slowly decaying solutions to the kinetic-Fokker-Planck equation
- Regularity for parabolic integro-differential equations with very irregular kernels
- A new regularization mechanism for the Boltzmann equation without cut-off
- Hitchhiker's guide to the fractional Sobolev spaces
- \(\Phi\)-entropy inequality and application for SDEs with jumps
- On a linear runs and tumbles equation
- Fractional operators with singular drift: smoothing properties and Morrey-Campanato spaces
- Anomalous transport of particles in plasma physics
- Fractional diffusion limit for collisional kinetic equations
- Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations
- Stability, convergence to self-similarity and elastic limit for the Boltzmann equation for inelastic hard spheres
- Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials
- Boltzmann equation for granular media with thermal force in a weakly inhomogeneous setting
- Ordinary differential equations, transport theory and Sobolev spaces
- Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
- Theory of function spaces
- Subgeometric rates of convergence of \(f\)-ergodic strong Markov processes
- Stability, convergence to the steady state and elastic limit for the Boltzmann equation for diffusively excited granular media
- One-parameter semigroups of positive operators
- Diffusion approximation for Fokker Planck with heavy tail equilibria: a spectral method in dimension 1
- On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials
- On the loss of continuity for super-critical drift-diffusion equations
- Uniform semigroup spectral analysis of the discrete, fractional and classical Fokker-Planck equations
- The Fokker-Planck equation with subcritical confinement force
- The weak Harnack inequality for the Boltzmann equation without cut-off
- Diffusion limit for kinetic Fokker-Planck equation with heavy tails equilibria: the critical case
- Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré
- Asymptotics for conservation laws involving Lévy diffusion generators
- Exponential trend to equilibrium for the inelastic Boltzmann equation driven by a particle bath
- Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
- Fractional diffusion limit for collisional kinetic equations: A moments method
- Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
- Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff
- Continuity of Solutions of Parabolic and Elliptic Equations
- Logarithmic Sobolev inequalities: Regularizing effect of Lévy operators and asymptotic convergence in the Lévy–Fokker–Planck equation
- Nonlinear SDEs driven by L\'evy processes and related PDEs
- Fractional Diffusion Limit for a Fractional Vlasov--Fokker--Planck Equation
- Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes
- Hölder estimates for advection fractional-diffusion equations
- On the differentiability of the solution to an equation with drift and fractional diffusion
- Well-posedness for the fractional Fokker-Planck equations
- A pointwise estimate for fractionary derivatives with applications to partial differential equations
- Sobolev Spaces
- Fractional Fokker-Planck equation