Geometric Singular Perturbation Theory for Fast-Slow PDEs

Abstract: Systems with multiple time scales appear in a wide variety of applications. Yet, their mathematical analysis is challenging already in the context of ODEs, where about four decades were needed to develop a more comprehensive theory based upon invariant manifolds, desingularization, variational equations, and many other techniques. Yet, for 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.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysis

Audience: researchers in the topic

"Partial Differential Equations and Applications" Webinar