Class Timings: Mondays and Wednesdays from 10:30 AM - 12:00 PM
Venue: Feynman Lecture Hall
First Meeting: 07 August 2023
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: Review of ODE theory; Fourier series and approximation; spectral methods for evolution PDEs; local/global wellposedness theory for nonlinear PDEs; Attractors in dynamical systems; Additional topics as per the interest of the instructor and students.
References:
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
G Schneider and H Uecker Nonlinear PDEs: A dynamical systems approach
Course Evaluation: 70% Homework + (30% Final viva exam or 30% Report/presentation)
- Teacher: Vishal Vasan