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DEPARTMENT OF MATHEMATICS, STATISTICS, AND PHYSICS

Victor Isakov, Distinguished Professor

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

 

Contact

 

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
  • Liang, Li  “Increasing stability in the inverse problem for the Schrodinger equation” PhD thesis, December 2015

 

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, Increasing stability for near field from the scattering amplitude, Contemp. Math., 640 (2015), 59-70
  • V. Isakov, J. Meyers, On the inverse doping profile problem, Inverse Problems and Imaging, 6 (2012) 465-486.
  • Isakov, V., On uniqueness of domains and general transmission conditions in inverse scattering, Comm. Math. Phys., 280 (2008) 843-858.
  • Isakov, V., Yamamoto,M., Wang, J.N.,Uniqueness and stability for the residual stress from one set of boundary data, Comm. Part. Diff. Equat., 32 (2007) 833-848.
  • 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.
  • I. Bouchouev, V. Isakov, N. Valdivia, Recovery of volatility coefficient by linearization, Quant. Finance, 2 (2002) 257-263.