MTH 627, Fall, 2004

MTH 627: Advanced Topics in Partial Differential Equations, Fall, 2004

LECTURE:	MWF 1500 - 1550	StAg 329	CRN 18214
Instructor:	R.E. Showalter	Kidder 330	show@math.oregonstate.edu

Here is information on Winter 2005 MTH 628.

We shall begin with a treatment of linear problems for partial differential equations of elliptic, parabolic or wave type and their realizations as unbounded operators or semigroups of operators in Hilbert space. This will include the development Sobolev spaces over an interval. In the second term, we shall develop related topics and corresponding applications to nonlinear problems and systems in higher dimension.

Prerequisite: MTH 513 or consent of instructor.
Final Exam: Thursday, December 9, 1400.
Textbook: Monotone Operators in Banach Space and Nonlinear Partial Differential Equations.

Schedule:
Chapter I. Linear Problems ... an Introduction
1. I.1 BVP in 1D, p. 1.(9/27)
2. generalized derivative, pp. 2 - 4.
3. anti-derivative, p. 5.
4. I.2 variational method, pp. 6 - 7.(10/4)
5. minimization principle, p. 8.
6. projections, Riesz map, p. 9.
7. Lax-Milgram theorem, p. 10. Exercises #1 and #2 due 10/18. (10/11)
8. Lions-Stampacchia theorem, pp. 11 - 12.
9. Examples: Dirichlet-Neumann BVP, pp. 13 - 14.
10. Examples: unilateral constraints, pp. 15 - 16. Exercises #3 due 10/25. (10/18)
11. unbounded operators, pp. 17 - 18.
12. m-accretive operators, pp. 19 - 20.
13. Cauchy problem , pp. 21 - 22. (10/25)
14. semigroups , pp. 22 - 23.
15. generation theorem, I , pp. 23 - 24.
16. generation theorem, II , pp. 25. Exercise #4 due 11/8. (11/01)
17. diffusion equation, pp. 26 - 27.
18. parabolic regularity , pp. 28 - 29.
19. wave equation, part 1 , pp. 30 - 31. (11/08)
20. wave equation, part 1b , pp. 31 - 32.
21. implicit evolution equation
22. Exercise 1 due (11/22) (11/15)
23. Example = Exercise 2
24. wave equation (continued from `implicit evolution equation')
25. Exercises (11/22)
27. Longitudinal vibrations, pp. 256 - 257. (11/29)
28. the 2x2 system, pp. 258 - 259.
29. Coming Attractions.