The approximation of the effective Hamiltonian is a challenging problem with a strong impact on many applications e.g. to the study of dynamical systems, weak KAM theory, homogenization, mass transfer problems. In this paper we present a numerical approximation of the variational approach proposed by C. Evans in [4], discuss its consistency and give some hints regarding its implementation. Finally, we compare this approach to the numerical implementation of the min-max formula proposed by Gomes and Oberman [6].
On a Variational Approximation of the Effective Hamiltonian / Falcone, Maurizio; Rorro, Marco. - (2008), pp. 719-726. ((Intervento presentato al convegno 7th European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2007) tenutosi a Graz, AUSTRIA nel SEP 10-14, 2007. [10.1007/978-3-540-69777-0_86].
On a Variational Approximation of the Effective Hamiltonian
FALCONE, Maurizio;RORRO, MARCO
2008
Abstract
The approximation of the effective Hamiltonian is a challenging problem with a strong impact on many applications e.g. to the study of dynamical systems, weak KAM theory, homogenization, mass transfer problems. In this paper we present a numerical approximation of the variational approach proposed by C. Evans in [4], discuss its consistency and give some hints regarding its implementation. Finally, we compare this approach to the numerical implementation of the min-max formula proposed by Gomes and Oberman [6].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.