The scaling limit for a stochastic PDE and the separation of phases

DOI10.1007/BF01213390zbMath0834.60066MaRDI QIDQ1893903

Tadahisa Funaki

Publication date: 12 March 1996

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

stochastic differential equationseparation pointstochastic partial differential equationsteady state problem

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics (82C24)

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Cites Work

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• The hydrodynamic limit for a system with interactions prescribed by Ginzburg-Landau type random Hamiltonian
• Stochastically perturbed Landau-Ginzburg equations
• Laplace approximations for sums of independent random vectors. II: Degenerate maxima and manifolds of maxima
• Reaction-diffusion equations for interacting particle systems
• Solutions of a stochastic differential equation forced onto a manifold by a large drift
• Infinite-dimensional dynamical systems in mechanics and physics
• The reversible measures of multi-dimensional Ginzburg-Landau type continuum model
• Regularity properties for stochastic partial differential equations of parabolic type
• Travelling fronts in nonlinear diffusion equations
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Interface motion in models with stochastic dynamics
• Spatial patterns when phases separate in an interacting particle system
• Blowup for the heat equation with a noise term
• Brownian fluctuations of the interface in the \(D=1\) Ginzburg-Landau equation with noise
• Slow-motion manifolds, dormant instability, and singular perturbations
• Motion by curvature by scaling nonlocal evolution equations
• Degenerative convergence of diffusion process toward a submanifold by strong drift
• Bistable Reaction-Diffusion Equations and Excitable Media
• Functional Integration and Partial Differential Equations. (AM-109)
• Random Perturbations of Reaction-Diffusion Equations: The Quasi-Deterministic Approximation
• Large fluctuations for a nonlinear heat equation with noise
• Phase transitions and generalized motion by mean curvature
• Glauber evolution with Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• The generation and propagation of internal layers
• Dynamical Fluctuations at the Critical Point: Convergence to a Nonlinear Stochastic PDE
• Intermediate spaces and interpolation, the complex method

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