Stochastic homogenization of viscous superquadratic Hamilton–Jacobi equations in dynamic random environment
نویسندگان
چکیده
We study the qualitative homogenization of second-order Hamilton–Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient), we establish a homogenization result and characterize the effective Hamiltonian for arbitrary (possibly degenerate) elliptic diffusion matrices. The result extends previous work that required uniform ellipticity and space-time homogeneity for the diffusion.
منابع مشابه
Periodic approximations of the ergodic constants in the stochastic homogenization of nonlinear second-order (degenerate) equations
We prove that the effective nonlinearities (ergodic constants) obtained in the stochastic homogenization of Hamilton-Jacobi, “viscous” Hamilton-Jacobi and nonlinear uniformly elliptic pde are approximated by the analogous quantities of appropriate “periodizations” of the equations. We also obtain an error estimate, when there is a rate of convergence for the stochastic homogenization.
متن کاملLarge time behavior of solutions of viscous Hamilton-Jacobi equations with superquadratic Hamiltonian
We study the long-time behavior of the unique viscosity solution u of the viscous Hamilton-Jacobi Equation ut−∆u+|Du| m = f in Ω×(0,+∞) with inhomogeneous Dirichlet boundary conditions, where Ω is a bounded domain of RN . We mainly focus on the superquadratic case (m > 2) and consider the Dirichlet conditions in the generalized viscosity sense. Under rather natural assumptions on f, the initial...
متن کاملA Short Proof of the C–regularity of Viscosity Subsolutions for Superquadratic Viscous Hamilton-jacobi Equations and Applications
Recently I. Capuzzo Dolcetta, F. Leoni and A. Porretta obtain a very surprising regularity result for fully nonlinear, superquadratic, elliptic equations by showing that viscosity subsolutions of such equations are locally Hölder continuous, and even globally if the boundary of the domain is regular enough. The aim of this paper is to provide a simplified proof of their results, together with a...
متن کاملA PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
متن کاملOn the Large Time Behavior of Solutions of the Dirichlet problem for Subquadratic Viscous Hamilton-Jacobi Equations
In this article, we are interested in the large time behavior of solutions of the Dirichlet problem for subquadratic viscous Hamilton-Jacobi Equations. In the superquadratic case, the third author has proved that these solutions can have only two different behaviors: either the solution of the evolution equation converges to the solution of the associated stationary generalized Dirichlet proble...
متن کامل