PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Tianyou Zhang.

Title:Generic solutions of PDEs
Seminar:Hyperbolic and Mixed Type PDEs Seminar
Speaker:Alberto Bressan, Penn State
Abstract:
ABSTRACT: For arbitrary smooth initial data, the solution of a hyperbolic PDE can exhibit wild behavior. However, using differential geometric methods, sometimes one can prove that "most" solutions are in fact quite nice. In other words, if we remove a (topologically small) set of initial data leading to pathological behavior, all the remaining solutions have a high degree of regularity. For example, the solution to a conservation law with smooth initial data can develop countably many shocks. But for an open dense set of C^2 initial data only finitely many shocks appear, located along smooth curves in the t - x plane, with finitely many intersection points. This talk will review some basic ideas and techniques in the generic theory of PDEs, and discuss some possible future applications.

Room Reservation Information

Room Number:MB216
Date:09 / 23 / 2014
Time:10:00am - 10:50am