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Inverse problems for real principal type operators

Recent developments in microlocal analysis October 14, 2019 - October 18, 2019

October 17, 2019 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Mikko Salo (University of Jyväskylä)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Inverse boundary value problem

  • real principal type operator

  • propagation of singularities

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video
Abstract

We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems. This is joint work with Lauri Oksanen (UCL), Plamen Stefanov (Purdue) and Gunther Uhlmann (Washington / IAS HKUST).

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