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Mathematics Colloquium I.

Speaker: Vishal Vasan.

Affiliation: ICTS Bengaluru.

Date and Time: Wednesday 23 October, 2:15 pm - 3:15 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Two unexpected applications of boundary value problems.

Abstract: Partial differential equations (PDE) and their boundary value
problems (BVP) arise naturally in a number of applications. Typically the
system of interest is modelled by a PDE/BVP. In this talk, I will present
two unexpected applications of BVPs where the original system does not
immediately indicate their importance. The first application comes from
the study of a particle moving in a fluid whose motion is modelled by a
finite dimensional system. The analysis will imply a natural
interpretation to the half derivative in terms of boundary-value problems.
The second application comes from the classical study of dispersive shock
waves (DSWs). DSWs are specific solutions to nonlinear dispersive
equations. However, I will present a BVP for a linear equation which
reproduces a number of DSW features. This raises an important question on
how to match experimental DSWs with particular nonlinear models:
qualitative comparisons do not suffice.

Vishal Vasan: ICTS Bengaluru.: Mathematics Colloquium