MA 606

Canonical forms of linear second order PDEs. Ill-posed and well-posed problems. General framework for linear PDEs: selfadjoint 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, and dispersion and solitons. <br>