Partial Differential Equations II

4 Credits.

This course is the second in the sequence about the general theory of PDEs. It focuses on time-dependent equations. It includes: Space-time Banach spaces. Linear 2nd order parabolic using Galerkin approximations. Linear 2nd order hyperbolic using Galerkin approximations. Semigroup theory and application to linear parabolic and hyperbolic equations. Nonlinear equations of Schr\"odinger/Wave type. Basic 2nd order semilinear wave equations. Systems of nonlinear hyperbolic equations. Conservation laws. Applications to equations coming from physics (Examples: Euler, Navier-Stokes, Einstein, etc...)