CRM: Centro De Giorgi
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New trends in Partial Differential Equations

Eigenvalues of dissipative boundary problems

speaker: Vesselin Petkov (IMB, Université de Bordeaux, France)

abstract: We study the localisation and the existence of the eigenvalues of the generator of a semigroup of contraction related to dissipative boundary problems for the wave equation and Maxwell system. The spectrum of the generator in the left half plane is formed by isolated eigenvalues with finite multiplicities and the corresponding solutions have an exponentially decreasing global energy. The localisation of such eigenvalues is important for the inverse scattering problems. We show that the eigenvalues are localisated in parabolic neighborhoods of the real axis or the imaginary one. For strictly convex obstacles we obtain a more precise result. Finally for the ball we establish a Weyl formula for the counting function of the eigenvalues.

Thu 6 Oct, 11:50 - 12:35, Aula Dini
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