Exponential convergence of solutions for random Hamilton–Jacobi equations

We show that for a family of randomly kicked Hamilton–Jacobi equations on the torus, almost surely, the solution of an initial value problem converges exponentially fast to the unique stationary solution. Combined with the earlier results of the authors, this completes the program in the multi-dimen...

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Bibliographic Details
Published in:Stochastic partial differential equations : analysis and computations 2020-09, Vol.8 (3), p.544-579
Main Authors: Iturriaga, Renato, Khanin, Konstantin, Zhang, Ke
Format: Article
Language:English
Subjects:
Boundary value problems
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Convergence
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Partial Differential Equations
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Toruses
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Summary:We show that for a family of randomly kicked Hamilton–Jacobi equations on the torus, almost surely, the solution of an initial value problem converges exponentially fast to the unique stationary solution. Combined with the earlier results of the authors, this completes the program in the multi-dimensional setting started by E, Khanin, Mazel and Sinai in the one-dimensional case.
ISSN:2194-0401
2194-041X
DOI:10.1007/s40072-019-00153-7