The Department of Mathematics Colloquium series continues on Thursday, November 17 with Dr. Hans Engler of Georgetown University presenting his research, Asymptotic Self-Similarity for Solutions of Integro-Differential Equations
This talk will be about partial integrodifferential equations that generalize the heat equation as well as the wave equation. In both special cases, as time becomes large, the solution attains a universal shape. For the heat equation, the asymptotic shape is known to be a Gaussian normal distribution, centered at the origin and with standard deviation equal to the square root of time. For the wave equation, the asymptotic “shape” is a distribution that is supported on or inside the sphere with radius equal to time. The question will be studied when and in which sense solutions of the general problem given above are asymptotic to a limiting profile, and at which rates this will happen. In the talk, I shall identify all possible limiting profiles and associated rates. It will also be shown that all these limits actually occur for suitable kernels. A naturally occurring requirement is that an integral kernel occurring in the equation is regularly varying in the sense of Karamata.
Refreshments will be served at 3:30.
Contact Matthew Pascal at {mpascal@towson.edu} or x43308 for further information
