Math 285G (Topics in Partial Differential Equations).
Lectures: MWF 11:30am-12:20pm in MS 6118.
Instructor: Monica Visan, MS 6167. Email address: firstname.lastname@example.org
Office Hours: just walk in.
Topics: We investigate local and global properties of solutions
to the focusing Klein-Gordon equation in three space dimensions, with
emphasis on the blowup/scattering dychotomy. The lectures will cover
- Strichartz estimates and local well-posedness.
- The groundstate solution.
- The Payne-Satinger criterion.
- Scattering "below" the groundstate.
- Center, stable and unstable manifolds in hyperbolic dynamics.
- The Lyapunov-Perron and Hadamard methods.
- The one-pass theorem.
- K. Nakanishi and W. Schlag, Invariant manifolds and dispersive
Hamiltonian evolution equations. Zurich
Lectures in Advanced Mathematics. European Mathematical Society (EMS),
Homework: There will be a small number of homework problems, whose completion is required to pass the class.