On a Burgers type nonlinear equation perturbed by a pure jump Lévy noise in \(\mathbb R^d\)

DOI10.1016/j.bulsci.2011.07.015zbMath1247.60096OpenAlexW2038119546MaRDI QIDQ441898

Bin Xie, Jiang-Lun Wu

Publication date: 8 August 2012

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2011.07.015

zbMATH Keywords

fundamental solutionexistence and uniquenessBurgers type nonlinear equationLévy spacestable-like generator of variable ordertime white noise

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (13)

Stochastic PDEs with heavy-tailed noise ⋮ Solving a nonlinear fractional stochastic partial differential equation with fractional noise ⋮ On a stochastic nonlocal conservation law in a bounded domain ⋮ Asymptotics of stochastic Burgers equation with jumps ⋮ Solving a non-linear stochastic pseudo-differential equation of Burgers type ⋮ Solving a nonlinear fractional SPDE with spatially inhomogeneous white noise ⋮ On a nonlinear stochastic pseudo-differential equation driven by fractional noise ⋮ Impacts of Gaussian noises on the blow-up times of nonlinear stochastic partial differential equations ⋮ Stochastic nonlocal conservation laws on whole space ⋮ On a fractional SPDE driven by fractional noise and a pure jump Lévy noise in \(\mathbb{R}^d\) ⋮ Martingale and weak solutions for a stochastic nonlocal Burgers equation on finite intervals ⋮ On a mixed fractional Burgers type equation with polynomial nonlinearity and perturbed by fractional Brownian sheet ⋮ A Petrov-Galerkin finite element method using polyfractonomials to solve stochastic fractional differential equations

Cites Work

• Unnamed Item
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• Solving a non-linear stochastic pseudo-differential equation of Burgers type
• Regularity results for stable-like operators
• On a stochastic nonlinear equation arising from 1D integro-differential scalar conservation laws
• SPDEs driven by Poisson random measure with non Lipschitz coefficients: existence results
• One-dimensional stochastic Burgers equation driven by Lévy processes
• Time irregularity of generalized Ornstein-Uhlenbeck processes
• Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise
• The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels
• Uniqueness in law for pure jump Markov processes
• Fractal Burgers equations
• Burgers-KPZ turbulence. Göttingen lectures
• Stable-like processes: Construction of the transition density and the behavior of sample paths near \(t=0\)
• On Markov process generated by pseudodifferential operator of variable order
• Invariant measures for Burgers equation with stochastic forcing
• The heat equation with Lévy noise
• On the stochastic Burgers' equation in the real line
• Pseudo differential operators with negative definite symbols of variable order
• Stochastic partial differential equation driven by stable noise
• On \(L^ {p}\)-solutions of semilinear stochastic partial differential equations.
• A remark on non-local operators with variable order
• On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension
• The heat equation with time-independent multiplicative stable Lévy noise
• Regularity of a fractional partial differential equation driven by space-time white noise
• Lévy measure with generalized polar decomposition and the associated sde with jumps
• Symmetric Stable Laws and Stable-Like Jump-Diffusions
• Stochastic burgers equation with correlated noise
• Stochastic Partial Differential Equations with Levy Noise
• Stochastic Equations in Infinite Dimensions

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