MA606
Partial Differential Equations II
0.5 Credit

Canonical forms of linear second order PDEs. Ill-posed and well-posed problems. General frameworks for linear PDEs: self-adjoint and positive definite linear operators, minimization principle, Rayleigh quotient, Eigenfunction series. Green's functions in the planar case and spatial case and higher dimensional; delta-function in higher dimensions. Additional topics may include: Finite elements and weak solutions. Linear and nonlinear evolution equations, linearization and stability. Heat and forced heat equations, maximum principle. Nonlinear diffusion. Dispersion and solitons.