I am mainly interested in Inverse Problems for Hyperbolic PDEs, in
the one dimensional and the multidimensional cases. I study the
uniqueness, continuous dependence, inversion, and related theoretical
questions, for these inverse problems. I also have some publications
on geometry, probability and economics.
List Of Publications (updated on January 22, 2009)
Recovering a function from its spherical mean values in two and three dimensions, (with D Finch), in Photoacoustic imaging and spectroscopy, edited by Lihong Wang, CRC Press (2009).
A remark on unique continuation along and across lower dimensional planes for the wave equation, Math. Meth. Applied Sciences, Vol 36, 246-252 (2009).
The d-th linear polarization constant of R^d, (with YJ Leung and Wenbo Li), Journal of Functional Analysis, Vol 255, Issue 10, 2861-2871 (2008).
Inverse problems for the wave equation with a single coincident source-receiver pair, Inverse Problems 24, 015012 (2008).
Spectral analysis of Brownian motion with jump boundary, (with YJ Leung and Wenbo Li), Proceedings of the AMS, Vol 136, 4427-4437 (2008).
The spherical mean value operator with centers on a sphere, (with D Finch), Inverse Problems Vol 23 No 6, S37-S49 (2007).
Inversion of spherical means and the wave equation in even dimensions (with D Finch and M Haltmeier), SIAM J Appl Math Vol 68 Issue 2, pages 392-412 (2007).
Optimal ellipsoids and decomposition of positive definite matrices (with YJ Leung and W Li), Journal of Mathematical Analysis and Applications, Volume 331, Issue 2, 1452-1466 (2007).
The range of the spherical mean value operator (with David Finch), Inverse Problems 22 (2006) 923-938.
Trace identities for solutions of the wave equation with initial data supported in a ball, (with D. Finch), Math Meth Appl Sciences, Volume 28, Issue 16(2005),1897-1917.
Determining a function from its mean values over a family of spheres , (with D. Finch and S. Patch), SIAM J Math Analysis, Vol 35, No 5, pp 1213-1240 (2004).
An inverse problem for a layered medium with a point source , Inverse Problems 19, 497-506, (2003).
A One Dimensional Inverse Problem For A Hyperbolic System With Complex Coefficients, Inverse Problems, 17, 1401-1417 (2001).
Characterization Of Transmission Data For Webster's Horn Equation, Inverse Problems, 16, L9-L24 (2000).
Inversion Of Spherically Symmetric Potentials from Boundary Data For The Wave Equation, Inverse Problems, 14, 999-1007 (1998).
Potential Inversion From Transmission Data For The One Dimensional Wave Equation, Wave Motion, 25, 319-329 (1997).
Some Results On Inverse Obstacle Problems For The Wave Equation , Algebra i Analiz 8 (1996), no. 2, 157-161, translation in St. Petersburg Math. J., 8, 303-306, (1997).
Impedance Inversion From Transmission Data For the Wave Equation (with Paul Sacks), Wave Motion, 24, 263-274 (1996).
An inverse problem for the wave equation in the half plane , Inverse Problems , 9, 433-441 (1993).
An inverse impedance transmission problem for the wave equation, Communications in PDE, 18, (1993), 583-600.
Numerical solution of a timelike Cauchy problem for the wave equation (with M. Klibanov), Mathematical Methods in the Applied Sciences, 15, (1992), 559-570.
Dynamic Pricing and Ordering Decisions by a Monopolist (with A. Rajan and R. Steinberg), Management Science, Vol. 38, No. 2, (1992), 240 - 262.
Property C and an inverse problem for a hyperbolic equation (with A.G. Ramm), Journal of Mathematical Analysis and Applications, Vol. 156, No. 1, (1991), 209-219.
Reconstruction for an inverse problem for the wave equation , Inverse Problems, 6 (1990), 91-98.
On the relation between the wavefront sets of the scatterer and the data (W.W. Symes), Inverse Problems, 4(1988), L21-22.
A linearised inverse problem for the wave equation, Communications in PDE, 13, 573-601 (1988).
Uniqueness for an inverse problem for the wave equation (with W.W. Symes), Communications in PDE, 13, 87-96 (1988).
Send comments to rakesh@udel.edu .