Victor Isakov

Victor Isakov, Distinguished Professor


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

Contact

Awards

WSU Excellence in Research Award ( 2001)

PhD Students

D. Aralummalige (current)
N. Kim (current)
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.

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, "Uniqueness of recovery of some quasilinear partial differential equations", Comm. Part. Diff. Equat., 26 (2001) 1947-1975.
  • I. Bouchouev, V. Isakov, N. Valdivia, "Recovery of volatility coefficient by linearization", Quant. Finance, 2 (2002), 257-263.
  • O. Imanuvilov, V. Isakov, 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, "Carleman estimates and applications to inverse problems", Milan J. Math., 72 (2004), 249-271.
  • V. Isakov, M. Yamamoto, J.-N. Wang, "Uniqueness and stability for the residual stress from one set of boundary data", Comm. Part. Diff. Equat. (to appear).