Manchester Applied Mathematics and Numerical Analysis Seminars

Spring 1999

February 3, 1999, 4.00 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)

Multidimensional inverse boundary spectral problems: Uniqueness and Stability

Prof. Slava Kurylev, Dept. of Mathematical Sciences, Loughborough University

In 1954 I.M. Gel'fand, generalising a recent result for the 1D inverse problem, formulated the following inverse problem: In a given domain consider a Schrodinger operator with unknown potential. Assume that we know values on the boundary of the Green's function (at different frequencies) which correspond to the Schrodinger operator under consideration. Do these data determine the potential uniquely? A more general variant of the problem deals with an anisotropic elliptic operator and the question is that of the determination of (as many as possible) unknown coefficients of this operator from the knowledge of the behavior of its Green's function on the boundary. In the talk we address this question of uniqueness for the general operator as well as for some specific ones, e.g acoustic or Schrodinger operators.We also discuss some stability issues which are particularly important for applications, i.e. to which extent the knowledge of only incomplete erratic data determines (at least approximately) unknown coefficients.

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For further info contact either Matthias Heil (, Mark Muldoon ( the seminar secretary (Tel. 0161 275 5800).

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