Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation |
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| Authors: | Denis Borisov |
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| Institution: | a Department of Physics and Mathematics, Bashkir State Pedagogical University, October rev. st., 3a, 450000, Ufa, Russia
b Department of Mathematics, Faculdade de Motricidade Humana (TU Lisbon) and Group of Mathematical Physics of the University of Lisbon, Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, P-1649-003 Lisboa, Portugal |
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| Abstract: | We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the damping term in a unique fashion. We also derive a trace formula for this problem. |
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| Keywords: | primary 35P15 secondary 35J05 |
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