Research Interests

I am 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.
 

List Of Publications (updated on November 11, 2008)

1. 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).

2. Inverse problems for the wave equation with a single coincident source-receiver pair, Inverse Problems 24, 015012 (2008).

3. Spectral analysis of Brownian motion with jump boundary, (with YJ Leung and Wenbo Li), Proceedings of the AMS, Vol 136, 4427-4437 (2008).

4. A remark on unique continuation along and across lower dimensional planes for the wave equation, to appear in Mathematical Methods Applied Sciences (2008).

5. Recovering a function from its spherical mean values in two and three dimensions, (with D Finch), to appear in Photoacoustic imaging and spectroscopy, edited by Lihong Wang, CRC Press (2008).

6. The spherical mean value operator with centers on a sphere, (with D Finch), Inverse Problems Vol 23 No 6, S37-S49 (2007).

7. 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).

8. 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).

9. The range of the spherical mean value operator (with David Finch), Inverse Problems 22 (2006) 923-938.

10. 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.

11. 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).

12. An inverse problem for a layered medium with a point source , Inverse Problems 19, 497-506,  (2003).

13. A One Dimensional Inverse Problem For A Hyperbolic System With Complex Coefficients,  Inverse Problems, 17,  1401-1417  (2001).

14. Characterization Of Transmission Data For Webster's Horn Equation, Inverse Problems, 16, L9-L24 (2000).

15. Inversion Of Spherically Symmetric Potentials from Boundary Data For The Wave Equation, Inverse Problems, 14, 999-1007 (1998).

16. Potential Inversion From Transmission Data For The One Dimensional Wave Equation,  Wave Motion, 25, 319-329 (1997).

17. 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).

18. Impedance Inversion From Transmission Data For the Wave Equation (with Paul Sacks), Wave Motion, 24, 263-274 (1996).

19. An inverse problem for the wave equation in the half plane ,  Inverse Problems , 9, 433-441 (1993).

20. An inverse impedance transmission problem for the wave equation, Communications in PDE,  18, (1993), 583-600.

21. Numerical solution of a timelike Cauchy problem for the wave equation (with M. Klibanov), Mathematical Methods in the Applied Sciences, 15, (1992), 559-570.

22. Dynamic Pricing and Ordering Decisions by a Monopolist (with A. Rajan and R. Steinberg),  Management Science, Vol. 38, No. 2, (1992), 240 - 262.

23. 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.

24. Reconstruction for an inverse problem for the wave equation , Inverse Problems, 6 (1990), 91-98.

25. On the relation between the wavefront sets of the scatterer and the data (W.W. Symes), Inverse Problems, 4(1988), L21-22.

26. A linearised inverse problem for the wave equation, Communications in PDE, 13,  573-601 (1988).

27. 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   .