An Introduction to Partial Differential Equations
Semester: Spring Semester 2017
See also the official course catalogue and metaphor
Schedule Lectures
| Day | Time | Room |
|---|---|---|
| Wednesdays | 10-12 | HG.E.21 |
| Fridays | 11-12 | HG.E.21 |
A preliminary sketch of the course
- The method of characteristics for first order equations, linear and nonlinear, transport equation, Hamilton-Jacobi equation.
- Laplace equation, fundamental solution, harmonic functions and main properties, maximum principle. Poisson equation. Green functions. Perron method for the solution of the Dirichlet problem.
- Heat equation, fundamental solution, existence of solutions to the Cauchy problem and representation formulas, main properties, uniqueness by maximum principle, regularity.
Time permitting: Wave equation, existence of the solution, D'Alembert formula, solutions by spherical means, main properties.
Recommended bibliography
- L. Evans, Partial Differential Equations, AMS 2010 (2nd edition) (Ch. 1,2,3,6).
- D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1998, (3rd edition). (Ch. 1,2,3).
- E. Di Benedetto, Partial Differential Equations, Birkauser, 2010 (2nd edition), (Ch. 0,2,5,6).
- F. John, Partial Differential Equations, Springer, 1995.
- T. Rivière, Exploring the unknown: the work of Louis Nirenberg in Partial Differential Equations, Notices Amer. Math. Soc. 63 (2016), no. 2, 120-125.
- L. Evans, Partial differential equations, Princeton Companion to Applied Mathematics.
- F. Da Lio, Introduction to Partial Differential Equations, Lecture Notes, FS17.