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Averaging of the Hamilton-Jacobi equation in infinite dimensions and an application

Published online by Cambridge University Press:  17 February 2009

Shihong Wang  and
Zuoyi Zhou
Shihong Wang
Affiliation:
Institute of Mathematics, Fudan University, Shanghai, China
Zuoyi Zhou
Affiliation:
Institute of Mathematics, Fudan University, Shanghai, China
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Abstract

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We study the averaging of the Hamilton-Jacobi equation with fast variables in the viscosity solution sense in infinite dimensions. We prove that the viscosity solution of the original equation converges to the viscosity solution of the averaged equation and apply this result to the limit problem of the value function for an optimal control problem with fast variables.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 3 , January 2000 , pp. 372 - 385
Copyright
Copyright © Australian Mathematical Society 2000

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