### MA6007 NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

#### Course Details

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 Processes-Similarity 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 system

#### Course References:

Books:

J David Logan, An introduction to nonlinear partial differential equations, John Wiley and Sons, Inc., 1994