After successful completion of the course, students are able to explain applications of Hamilton-Jacobi equations. Moreover, they can explain solution concepts and solution theories for Hamilton-Jacobi equations (in particular visvosity solutions, explicit solution representations).

Hamilton-Jacobi equations are fully nonlinear PDEs of the form u_t + H(nabla u,x) = 0 and they apear in the following application fields: Hamilton mechanics, front propagation (in geometry and optics), control theory, differential game theory.Topic of the seminar:* (extended) mathod of characteristics for smooth solutions;* connection to hyperbolic conservation laws;* Hopf-Lax solution formula (for H(p) convex), Legendre trnasform;* method of vanishing viscosity;* viscosity solutions for H(p,x) not convex (based on a maximum principle, instead of integratin by parts onto test functions)

presentation by the participating students (blackboard or beamer),discussion of the weekly seminar by the whole "class",write-up of a seminar paper

Please consider the plagiarism guidelines of TU Wien when writing your seminar paper: https://www.tuwien.at/index.php?eID=dms&s=4&path=Richtlinien und Verordnungen/Lehre - Leitfaden zum Umgang mit Plagiaten.pdf

Timing to be arranged (TH 16:00 is just a first suggestion)

2nd organizational meeting 14.10.2021, 15:00, Sem 6A green

good oral presentation, written seminar report, regular participation

Not necessary

Additional literature* L.S. Evans, Partial Differential Equations, AMS, 1998 (§3, §10)* J.A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge UniversityPress, 1999* M.G. Crandall, H. Ishii, P.L. Lions, User's guide to viscosity solutions of 2nd oder PDEs, Bullelin of the AMS 27, 1992

partial differential equations