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 June 13, 2008)

1. The d-th linear polarization constant of R^d, (with YJ Leung and Wenbo Li), to appear in Journal of Functional Analysis (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), to appear in Proceedings of the AMS (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   .