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Global existence of solutions of an activator-inhibitor system
Averaging of time - periodic systems without a small parameter
1. | Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris, France |
2. | Département Terre-Atmosphère-Océan and, Laboratoire de Météorologie Dynamique du CNRS/IPSL, École Normale Supérieure, Paris, France |
3. | Laboratoire de Météorologie Dynamique du CNRS/IPSL, École Normale Supérieure, Paris, France |
4. | Institute of Geophysics and Planetary Physics, University of California, Los Angeles, United States |
Using these transformations, it is possible to correct the solution of an averaged system by recovering the oscillatory components of the original non-averaged system. In this framework, the inverse transformations are also defined explicitly by formal series; they allow the estimation of appropriate initial data for each higher-order averaged system, respecting the equivalence relation.
Finally, we show how these methods can be used for identifying and computing periodic solutions for a very large class of nonlinear systems with time-periodic forcing. We test the validity of our approach by analyzing both the first-order and the second-order averaged system for a problem in atmospheric chemistry.
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