SPACE-MODULATED STABILITY AND AVERAGED DYNAMICS

Luis Miguel Miguel Rodrigues (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this brief note we give a brief overview of the comprehensive theory, recently obtained by the author jointly with Johnson, Noble and Zumbrun, that describes the nonlinear dynamics about spectrally stable periodic waves of parabolic systems and announce parallel results for the linearized dynamics near cnoidal waves of the Korteweg–de Vries equation. The latter are expected to contribute to the development of a dispersive theory, still to come.

Mots clés: stability; periodic traveling waves

Domaines: Equations aux dérivées partielles [math.AP]

Luis Miguel Miguel Rodrigues. SPACE-MODULATED STABILITY AND AVERAGED DYNAMICS. Journées Équations aux dérivées partielles, 2015, Roscoff, France. Exposé No. 8. ⟨hal-01246521⟩