Advanced Partial Differential Equations

1.5 credits · Undergraduate

Classical linear PDEs; transport, Laplace, Poisson, heat, and wave equations. Scalar nonlinear first order equations, Hamilton-Jacobi, conservation laws, characteristics and notion of weak solutions. Representation of solutions, similarity solutions, Fourier transform, singular perturbation, travelling waves, power series solutions. Sobolev spaces, elliptic equations, Lax-Milgram, regularity, maximum principle. Linear evolution equations, parabolic and hyperbolic, semi-group theory. Additional topics as time permits.