Young measure approach to computing slowly advancing fast oscillations

abstract

• We offer a multiscale and averaging strategy to compute the solution of a singularly perturbed system when the fast dynamics oscillates rapidly; namely, the fast dynamics, rather than settling on a manifold of smaller order, forms cycle-like limits which advance along with the slow dynamics. We describe the limit as a Young measure with values being supported on the limit cycles, averaging with respect to which induces the equation for the slow dynamics. In particular, computing the tube of limit cycles establishes a good approximation for arbitrarily small singular parameters. Possible algorithms are displayed and concrete numerical examples are exhibited. 2008 Society for Industrial and Applied Mathematics.

authors

• Titi, Edriss

published proceedings

• MULTISCALE MODELING & SIMULATION

author list (cited authors)

• Artstein, Z., Linshiz, J., & Titi, E. S.

citation count

• 17

complete list of authors

• Artstein, Zvi||Linshiz, Jasmine||Titi, Edriss S

publication date

• January 2007

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM: Multiscale Modeling and Simulation  Journal

keywords

• Limit Cycles
• Multiscale Computation
• Singular Perturbations
• Young Measures

Digital Object Identifier (DOI)

• 10.1137/070687219

start page

• 1085

end page

• 1097

volume

• 6

issue

• 4

URL

• http://dx.doi.org/10.1137/070687219