### Victor Isakov, Distinguished Professor

Partial Differential Equations; PhD, Institute of Mathematics, USSR, 1973

### Awards

WSU Excellence in Research Award ( 2001)

### PhD Students

J. Powell, "Some Inverse Boundary Value Problems", PhD thesis,1992

A. Elayyan, "Some Inverse Problems in Parabolic Partial Differential Equations", PhD thesis, 1996

A. Sever, "On the Inverse Conductivity Problems", PhD thesis, 1996

M. Eller, "Uniqueness of Continuation Theorems", PhD thesis,1997

I. Bouchouev, "Inverse Parabolic Problems with Applications to Option Pricing", PhD thesis, 1997

N. Valdivia, "Inverse Problems in Scattering Theory and Acoustics", 2002.

J. Myers, "Inverse Doping Profile Analysis for Semiconductor Quality Control", PhD thesis, 2009

N. Kim, "Carleman jEstimates for the general Second Qrder Qperators and Applications to Inverse Problems", PhD thesis, 2010

D. Aralumallige Subbarayappa, "Stability of Continuation and Obstacle Problems in Acoustics and Electromagnetic Scattering", PhD thesis, 2010

D. Stewart (current)

### Research

My main research area is Inverse problems for Partial Differential
Equations. One looks for a coefficient or a source term from additional
boundary data. Lately I am working on inverse problems in elasticity
(identification of elastic parameters), in inverse scattering (looking for an
obstacle and boundary conditions from scattering data), in option pricing
(finding volatility of markets from current trading data), and in
semiconductor theory (looking for doping profile). A special topic of more
general nature is Carleman estimates for equations and systems.

### Selected Publications

- V. Isakov, O. Imanuvilov, M. Yamamoto, "An inverse problem for the dynamical Lame system with two sets of boundary data", Comm. Pure Appl. Math., 56 (2003), 1366-1382.
- V. Isakov, M. Yamamoto, J.N. Wang, "Uniqueness and stability for the residual stress from one set of boundary data", Comm. Part. Diff. Equat., 32 (2007), 833-848.
- V. Isakov, "On uniqueness of domains and general transmission conditions in inverse scattering", Comm. Math. Phys., 280 (2008) 843-858.
- V. Isakov, "On identification of the doping profile in semiconductors", Contemp. Math. AMS, 494 (2009), 123-137.
- V. Isakov, N. Kim, G. Nakamura, "Reconstruction of an unknow inclusion by thermography", Ann. Sc. Norm. Super Pisa, 9 (2010), 725-758.
- V. Isakov & N. Kim, "Weak Carleman estimates with two large parameters and applications to elasticity with residual stress", Discr. Cont. Dyn. Syst. A, 27 (2010), 799-827.