MA 876; Special Topics in Partial Differential Equations

Spring 2014

MWF 1:00-2:00pm


Instructor: 


Gene Wayne
Math Department
111 Cummington Street
Room 242
Phone: 353-1495
e-mail: cew@math.bu.edu

This spring MA 876 will focus on the use of dynamical systems methods to understand the qualitative behavior of solutions of partial differential equations. I plan to start out following Dan Henry's book. In particular, we'll discuss semigroup theory for sectorial operators, and their use in solving semilinear-PDE's. We'll also discuss invariant manifold theorems for PDE's, though I will probably follow the treatment in the more recent article of Chen, Hale and Tan, rather than Henry's approach. After that, we'll look at a number of applications - exactly which one's we choose will be determined by the interests of the participants. At the moment, the course is scheduled to meet at MWF from 1:00-2:00, but we usually reschedule it to meet twice a week, depending on the constraints of the participants. If you have any questions about this course, please don't hesitate to contact me.

References

Geometric Theory of Semilinear Parabolic Equations; D. Henry, Springer LNM vol. 840 (1981). Invariant Foliations for C1 Semigroups in Banach Spaces: X.-Y. Chen, J. Hale and B. Tan, J. Diff. Eqns, pp. 283-318 (1997).

I'll keep an updated reading list on the course webpage.

Grading: All students enrolled in the course will be expected to give at least two lectures on topics related to the course. Your grade will be based on these lectures.

File translated from TEX by TTH, version 1.60.