A probabilistic approach for nonlinear equations involving the fractional Laplacian and a singular operator

DOI10.1007/s11118-004-3264-9zbMath1069.60056OpenAlexW2054731695MaRDI QIDQ1775509

Benjamin Jourdain, Sylvie Méléard, Wojbor A. Woyczyński

Publication date: 3 May 2005

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-004-3264-9

zbMATH Keywords

propagation of chaossingular potentialinteracting particle approximationLévy process-driven nonlinear stochastic differential equationnonlinear and nonlocal evolution equation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Fractional derivatives and integrals (26A33) Applications of stochastic analysis (to PDEs, etc.) (60H30) Initial value problems for PDEs with pseudodifferential operators (35S10)

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Non-local conservation law from stochastic particle systems ⋮ GENERALIZED SOLUTIONS OF THE CAUCHY PROBLEM FOR SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS AND DIFFUSION PROCESSES ⋮ Two‐dimensional fractal Burgers equation with step‐like initial conditions ⋮ Derivation of Fokker-Planck equations for stochastic systems under excitation of multiplicative non-Gaussian white noise ⋮ Deep Ritz Method for the Spectral Fractional Laplacian Equation Using the Caffarelli--Silvestre Extension ⋮ From anomalous to classical diffusion in a nonlinear heat equation ⋮ Scaling limit of a kinetic inhomogeneous stochastic system in the quadratic potential ⋮ Dynamics and regularity for non-autonomous reaction-diffusion equations with anomalous diffusion ⋮ Well-posedness of some non-linear stable driven SDEs ⋮ Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density ⋮ Probabilistic approximation and inviscid limits for one-dimensional fractional conservation laws ⋮ Small stochastic perturbations in a general fractional kinetic equation ⋮ Non-uniqueness of weak solutions for the fractal Burgers equation ⋮ Fractal Hamilton-Jacobi-KPZ equations

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