MA 876; Special Topics in Partial Differential Equations

Spring 2014

MWF 1:00-2:00pm


Gene Wayne Math Department 111 Cummington Street Room 242 Phone: 353-1495 e-mail:

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.


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.

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