Review of first order equations and characteristics.
Weak solutions to hyperbolic equations - discontinuous solutions, shock formation, a formal approach to weak solutions, asymptotic behaviour of
shocks.
Diffusion ProcessesSimilarity methods, Fisher's equation, Burgers'
equation, asymptotic solutions to Burgers' equations.
Reaction diffusion equations-traveling wave solutions, existence of
solutions, maximum principles and comparison theorem, asymptotic
behaviour.
Elliptic equations - Basic results for elliptic operators, eigenvalue problems,
stability and bifurcation.
Hyperbolic systems – Elementary results.
- Teacher: chsrao Srinivasa Rao C H