MA876 - PDE Seminar - Spring 2018
Lectures: TR 11:00-12:15 in CAS 314
Announcements:
Content of Course:
This course will focus on methods for determining the point spectrum
of linear operators associated with nonlinear waves. I will begin with
motivation and an introduction to the relevant aspects of spectral
theory. Next I will introduce the Evans function, and discuss in
particular how it can be used to study slow-fast systems and
perturbations of eigenvalues. As time permits I will also discuss
recent developments in spatial dimensions greater than one. (Note:
these topics are tentative and subject to change as the semester
progresses.)
Here is the syllabus.
Course Format:
I will give the lectures at least until Spring Break. The remaining
lectures will be given by participants in the course. If you are
taking the course for credit, you are required to give at least two
lectures, and your grade will be based entirely on these lectures. If
you are auditing the course it is up to you whether or not you give
lectures, but please let me know by February 14 whether or not you
wish to do so. The topic of your lectures can be anything you like
that is related to the point spectrum of linear operators associated
with nonlinear waves. I'm happy to discuss your interests with you and
suggest a topic, if you wish.
Important Dates:
- By February 14: Initial discussion with me regarding your lecture topic.
- By February 28: Topic finalized and availability of dates for your lectures submitted.
- TBD After Spring Break: You give (at least) two lectures
References:
This course will draw from a variety of souces including
- Henry,
D. "Perturbation
of the boundary in boundary-value problems of partial differential
equations." London Mathematical Society Lecture Note Series,
318. Cambridge University Press, Cambridge, 2005.
- Kapitula,
T. "Stability
analysis of pulses via the Evans function: dissipative systems."
Dissipative solitons, 407–428, Lecture Notes in Phys., 661, Springer,
Berlin, 2005. A .pdf of the paper can be found on Todd's
webpage here.
- Kapitula, T. and Promislow,
K. "Spectral
and dynamical stability of nonlinear waves." Applied
Mathematical Sciences, 185. Springer, New York, 2013.
- Sandstede,
B. "Stability
of travelling waves." Handbook of dynamical systems, Vol. 2,
983-1055, North-Holland, Amsterdam, 2002. A .pdf of the paper can be
found on Björn's webpage here.
- Sandstede, B,
"The
Evans function: An example."
I will update this list as the semester progresses, for example to
include references that are relevant for the topics you choose for
your lectures.
Contact Information
Instructor: Margaret Beck
Office: MCS 228
Phone: 617-358-3314
Email: mabeck -at- bu.edu
Office Hours: Mondays 2:30-3:30, Thursdays 3:30-4:30, or by appointment
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