V5B8 - Selected Topics in Analysis - The vector field method and quasilinear wave equations

Summer Semester 2022

Dr. Dongxiao Yu
Instructor

Lectures

Office hours

Tue 14-15, Room 2.005, Endenicher Allee 60. Or by appointment.

Topics

In this course we will study the lifespans of solutions to some special types of quasilinear wave equations with small, smooth and localized initial data. Using the so-called ''vector field method'', we will prove several global or almost global existence results for quasilinear wave equations.

The prerequisites include basic real analysis and basic knowledge about partial differential equations.

Here is a tentative schedule.

Literature

Here are the lecture notes.

The following four books are recommended but not required:

My plan is to follow Chapter I and II in Sogge’s book and use the other three books as complements.

Exam

There will be an oral exam at the end of the semester. Further details will be forthcoming.

Important links

Basis page

Ecampus page