GSPT for Fast-Slow PDEs

Speaker: Prof. Dr. Christian Kühn
Affiliation: TU München (Germany)
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)

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Meeting ID: 530 867 8850 | PIN: 014005

Abstract. Systems with multiple time scales appear in a wide variety of applications. Yet, their mathematical analysis is challenging already in the context of ordinary differential equations (ODEs), where about four decades were needed to develop a more comprehensive theory based upon invariant manifolds, desingularization, variational equations, and many other techniques. This framework has become known as geometric singular perturbation theory (GSPT). Yet, for partial differential equations (PDEs) progress has been extremely slow due to many obstacles in generalizing several ODE methods. In my talk, I shall report on two recent advances for fast-slow PDEs, namely the extension of slow manifold theory for unbounded operators driving the slow variables, and the design of a blow-up method for PDEs, where normal hyperbolicity is lost. This is joint work with Maximilian Engel and Felix Hummel.

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