Venue: Feynman Lecture Hall
Class Timings: 11:00 AM to 12:30 PM, Mondays and Wednesdays
First Meeting: 03 August 2022
Course description: This course is aimed at students and researchers working in the field of nonlinear PDEs. We will focus on semilinear evolution equations arising in various branches of physics and engineering. The course will place emphasis on the interplay between the mathematical theory of wellposedness and the solution to concrete questions arising from applications (for example inverse problems/control/numerical methods for semilinear evolution equations). Selected topics include: well-posedness theory for nonlinear PDEs; spectral methods; observer problems; existence of attractors. Additional topics as per interest of the instructor and students.
- T Tao, Nonlinear Dispersive Equations: local and global analysis;
- R Temam, Infinite dimensional dynamical systems in mechanics and physics;
- C Doering, Applied analysis of Navier-Stokes;
- Schneider and Uecker, Nonlinear PDEs: A Dynamical Systems Approach
Students must have prior experience with PDEs (through coursework or research); preferably nonlinear models. Homeworks will involve simulations as well as proofs, so students must have experience solving ODEs numerically. Real and complex analysis will be extremely useful but we will develop the tools as necessary. Students are advised to talk to the instructor before registering.
- Teacher: Vishal Vasan