Analysis of Partial Differential Equations

Catalog description

Transport equation, Laplace equation, heat equation, wave equation, method of characteristics, Green’s functions, Newtonian potential, maximum principle, harmonic functions, Harnack’s inequality, Liouville’s theorem, heat kernel, fundamental solutions, method of descent, D’Alembert’s, Kirchoff’s, and Poisson’s formula, Sobolev spaces, Trace operators, ellipticity, Lax-Milgram, spectral theory, Galerkin approximations, interior elliptic regularity, boundary regularity, Riemann problem, shock solutions, rarefaction waves, Rankine-Hugoniot condition, energy method.