ICTS Course no.: MTH 247.5

Venue: Online

Class timings: Mondays and Wednesdays 2:00-3:30 (Additional tutorial TBD).

First meeting: 30th August 2021, last lecture in the second week of December. 

Course description: 

This course is aimed at students and researchers working in the field of nonlinear PDEs. We will focus on semilinear evolution equations (mostly scalar-valued) with the emphasis on (a) the mathematical theory behind such equations, (b) how this theory informs the development of numerical methods. Selected topics include: transform techniques for linear equations; spectral methods for evolution PDEs; wellposedness theory for nonlinear PDEs. Additional topics as per the interest of the instructor and students.

Prerequisites: Interested individuals should have prior experience with nonlinear PDEs and numerical methods (through coursework or research). A course in the real and complex analysis will be useful but not essential. Students should consult the instructor before registering.

Course structure: 50% Homework + 20% Report + 30% Final viva exam.

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
selected papers to be distributed in class