On stochastic diffusion equations and stochastic Burgers’ equations

DOI10.1063/1.531391zbMath0866.35149OpenAlexW1969554802MaRDI QIDQ5284378

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Publication date: 24 July 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531391

zbMATH Keywords

viscosity solutionstochastic heat equationwhite noisestochastic Burgers equationsHopf-Cole transformationstochastic Hamilton-Jacobi equationharmonic oscillator potentials

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Solutions to PDEs in closed form (35C05)

Related Items (9)

On \(L^ {p}\)-solutions of semilinear stochastic partial differential equations. ⋮ Averaging principle for one dimensional stochastic Burgers equation ⋮ Geometric properties of the Maxwell set and a vortex filament structure for Burgers equation ⋮ Mild solutions for the stochastic generalized Burgers-Huxley equation ⋮ Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations ⋮ Kolmogorov equations in infinite dimensions: well-posedness and regularity of solutions, with applications to stochastic generalized Burgers equations ⋮ О точности разностной схемы для уравнений Навье - Стокса ⋮ An approximate solution for stochastic Burgers' equation driven by white noise ⋮ Numerical simulations of nonlinear stochastic Newell-Whitehead-Segel equation and its measurable properties

Cites Work

• Stochastic oscillators
• The stochastic Burgers equation
• Stratified structure of the Universe and Burgers' equation -- a probabilistic approach
• The stochastic heat equation: Feynman-Kac formula and intermittence.
• The Cauchy problem for a nonlinear first order partial differential equation
• Dynamic Scaling of Growing Interfaces
• Classical mechanics, the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold
• Laplace asymptotic expansions of conditional Wiener integrals and generalized Mehler kernel formulas
• Hamiltonian systems with a stochastic force:nonlinear versus linear, and a girsanov formula
• Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation
• The burgers equation with a noisy force and the stochastic heat equation
• Approximate travelling waves for generalized KPP equations and classical mechanics
• The partial differential equation u_t + uu_x = μ_xx

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