MATE 6677   Partial Differential Equations

Time and place

LW 18:00--19:15, M-117.

Topics

Preliminaries, notation and terminology. Green's formula and integration by parts.

Diffusion and the heat equation. Solution on bounded domain in one dimension; formulation in higher dimensions. Uniqueness and maximum principle. Fundamental solution.

The Laplace equation. Well posed problems and uniqueness. Harmonic functions. Fundamental solution and Newtonian potential. Green function. Uniqueness in unbounded domains.

Scalar conservation laws and first-order equations. Linear transport equation. Weak solutions, jump condition, entropy condition. Method of characteristics for quasilinear equations.

The wave equation. One-dimensional wave equation. d'Alembert formula. The Cauchy problem, fundamental solution and strong Huygen's principle. Kirchhoff formula, Hadamard method of descent.

Further topics as time allows.

References

"Partial differential equations in action" by Sandro Salsa, Springer 2008.

"Partial differential equations" by L.C. Evans, AMS, 2000.

Grading policy

Homework, exams and/or presentations.

Homework   updated 17/09.

Last modified: Tue Sep 17 00:47:12 AST 2013