From Brownian-Time Brownian Sheet to a Fourth Order and a Kuramoto–Sivashinsky-Variant Interacting PDEs Systems

DOI10.1080/07362994.2011.598794zbMath1246.35068arXiv1007.5302OpenAlexW2034701350MaRDI QIDQ3114565

Hassan Allouba

Publication date: 19 February 2012

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.5302

zbMATH Keywords

random fieldsfractional Cauchy problemsBrownian-time processesBrownian-time Feynman-Kac formulaiterated Brownian sheetlinear systems of interacting fourth order PDEsnonlinear fourth order coupled PDEs

Mathematics Subject Classification ID

Random fields (60G60) Brownian motion (60J65) Integral representations of solutions to PDEs (35C15) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Probabilistic potential theory (60J45) Transition functions, generators and resolvents (60J35) Higher-order parabolic systems (35K41) Systems of nonlinear higher-order PDEs (35G50)

Related Items (6)

Global existence and pointwise estimates of solutions to generalized Kuramoto-Sivashinsky system in multi-dimensions ⋮ Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation ⋮ Time-fractional and memoryful \(\Delta^{2^{k}}\) SIEs on \(\mathbb{R}_{+}\times\mathbb{R}^{d}\): how far can we push white noise? ⋮ L-Kuramoto-Sivashinsky SPDEs in one-to-three dimensions: L-KS kernel, sharp Hölder regularity, and Swift-Hohenberg law equivalence ⋮ INTERACTING TIME-FRACTIONAL AND Δ^ν PDES SYSTEMS VIA BROWNIAN-TIME AND INVERSE-STABLE-LÉVY-TIME BROWNIAN SHEETS ⋮ L-Kuramoto-Sivashinsky SPDEs vs. time-fractional SPIDEs: exact continuity and gradient moduli, 1/2-derivative criticality, and laws

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