Some Inverse Problems in Hyperbolic Partial Differential Equations
Speaker 
Shri Manmohan Vashisth
Research Scholar, TIFRCAM, Bangalore


When 
Feb 27, 2018
from 02:00 PM to 03:00 PM 
Where  LH006 
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Abstract: In this talk, we will focus on three inverse problems in hyperbolic partial differential equations.
In the first part, we consider the inverse problem of determining timedependent vector and scalar potentials appearing in the wave equation in space dimension n ≥ 3 from information about the solution on a suitable subset of the boundary cylinder.
In the second part, we consider an inverse boundary value problem for a nonlinear wave equation of divergence form with space dimension n ≥ 3. We study the unique determination of quadratic nonlinearity appearing in the wave equation from measurements of the solution at the boundary of the spacial domain over finite time interval.
In the third part, we address the inverse problem of determining the density coefficient of a medium by probing it with an external point source and by measuring the responses at a single point (different from the source point) for a certain period of time.
The first part of the talk is joint work with Venky Krishnan, and the second part is done jointly with Gen Nakamura.