Communications on Pure and Applied Analysis (CPAA)

On the convergence of singular perturbations of Hamilton-Jacobi equations

Pages: 1363 - 1377, Volume 9, Issue 5, September 2010      doi:10.3934/cpaa.2010.9.1363

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Claudio Marchi - Dipartimento di Matematica Pura ed Applicata, Università di Padova, via Trieste 63, 35121 Padova, Italy (email)

Abstract: This paper is devoted to singular perturbation problems for first order equations. Under some coercivity and periodicity assumptions, we establish the uniform convergence and we provide an estimate of the rate of convergence, which we consider the main result of the paper.
    We shall also show that our results apply to the homogenization problem for coercive and periodic equations. Finally, some examples arising in optimal control and differential games theory will be discussed.

Keywords:  Singular perturbations, viscosity solutions, Hamilton-Jacobi equations, ergodicity, homogenization, rate of convergence.
Mathematics Subject Classification:  Primary: 35B25; Secondary: 49L25, 35B27.

Received: September 2009;      Revised: December 2009;      Available Online: May 2010.