On the resonances and the inverse scattering problem for perturbed wave equations

We consider finite energy solutions of the perturbed wave equation □u+q(x,t)u=0 where x ε ℝ3, t ε ℝ. We analyse two type of problems: First, we give suitable conditions on q and we prove that there exist infinite many "resonances" λj associated with q. Secondly, we study the problem of det...

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Bibliographic Details
Published inPartial Differential Equations pp. 236 - 244
Main Author Menzala, Gustavo Perla
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 19.11.2006
SeriesLecture Notes in Mathematics
Subjects
Bounded Solution
Compact Operator
Complex Pole
Green Function
Wave Equation
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ISBN3540501118
9783540501114
ISSN0075-8434
1617-9692
DOI10.1007/BFb0100795

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Summary:We consider finite energy solutions of the perturbed wave equation □u+q(x,t)u=0 where x ε ℝ3, t ε ℝ. We analyse two type of problems: First, we give suitable conditions on q and we prove that there exist infinite many "resonances" λj associated with q. Secondly, we study the problem of determining q from the scattering operator associated with the above equation. We describe a uniqueness result on the inverse scattering problem and state some open problems on the subject.
Bibliography:This is an expanded version on a one-hour invited Lecture presented by the author at the Latin American School of Mathematics (ELAM) held at IMPA (July 1986), Rio de Janeiro, RJ, Brasil.
ISBN:3540501118
9783540501114
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0100795