LECTURE: MWF 1100 -- 1150 Gilkey 100 CRN 17237 Instructor: R.E. Showalter Kidder 298B show@math.oregonstate.edu
Prerequisite: MTH 512 or consent of instructor.
Final Exam: TBA
Textbook: Hilbert Space Methods for Partial Differential Equations.
The textbook is available online at this site courtesy of the Electronic Journal of Differential Equations.Elements of Hilbert Space presents the elementary Hilbert space theory that is needed for the book.Schedule:
Distributions and Sobolev Spaces is an introduction to distributions and Sobolev spaces. The latter are the Hilbert spaces in which we shall show various problems are well-posed.
Boundary Value Problems is an exposition of linear elliptic boundary value problems in variational form.
First Order Evolution Equations is an exposition of the generation theory of linear semigroups of contractions and its applications to solve initial-boundary value problems for partial differential equations.
1. Linear algebra pp. 1-3. (9/24)
2. pp. 3-6.
3. Convergence and continuity pp. 6-9.
4. Operators and Dual space pp. 9-13. (10/1)
5. Hilbert space and `preview' pp. 13-14.
6. Minimization.
7. Projection, variational inequalities, and BVP (10/8)
8. L^2, Regularization and Distributions pp. 31-33.
9. Derivatives, Sobolev space pp. 33-41.
10. Trace pp. 41-45. (10/15)
11. Trace pp. 46.
12. Trace pp. 47.
13. Dirichlet boundary value problem pp. 59-61. (10/22)
14. Neumann and Robin boundary value problems pp. 75-76.
15. From weak to strong formulation
16. Lax-Milgram theorem pp. 61-62. (10/29)
17. abstract Green's theorem pp. 62-65.
18. Examples pp. 69-70. Exercises.
19. Oblique derivative problem. pp. 70-72. (11/05)
20. Interface problem. pp. 70-72.
21. Concentrated capacity/mass.
22. Concentrated conductivity. pp. 72-73.(11/12)
23. Elliptic equations. pp. 74-75.
24. ---
25. Review (11/19)
26. V-ellipticity pp. 75-77.
27. Periodic BVP. (11/26)