Document Zbl 1358.35012

Jing, Wenjia; Souganidis, Panagiotis E.; Tran, Hung V.

Stochastic homogenization of viscous superquadratic Hamilton-Jacobi equations in dynamic random environment. (English) Zbl 1358.35012

Res. Math. Sci. 4, Paper No. 6, 20 p. (2017).

Summary: 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.

Cited in 6 Documents

MSC:

35B27	Homogenization in context of PDEs; PDEs in media with periodic structure
70H20	Hamilton-Jacobi equations in mechanics
49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games

Keywords:

stochastic homogenization; Hamilton-Jacobi equations; viscosity solutions; dynamic random environment; time-dependent Hamiltonian; convex analysis

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References:

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