Abstract
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.
Keywords
- Wave Equation
- Green Function
- Compact Operator
- Bounded Solution
- Complex Pole
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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.
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© 1988 Springer-Verlag
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Menzala, G.P. (1988). On the resonances and the inverse scattering problem for perturbed wave equations. In: Cardoso, F., de Figueiredo, D.G., Iório, R., Lopes, O. (eds) Partial Differential Equations. Lecture Notes in Mathematics, vol 1324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100795
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DOI: https://doi.org/10.1007/BFb0100795
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