Asymptotic distribution of eigenfrequencies for damped wave equations

Johannes Sjöstrand

Journées équations aux dérivées partielles (2000)

  • Volume: 36, Issue: 5, page 1-8
  • ISSN: 0752-0360

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Sjöstrand, Johannes. "Asymptotic distribution of eigenfrequencies for damped wave equations." Journées équations aux dérivées partielles 36.5 (2000): 1-8. <http://eudml.org/doc/93393>.

@article{Sjöstrand2000,
author = {Sjöstrand, Johannes},
journal = {Journées équations aux dérivées partielles},
keywords = {Birkhoff limits; Weyl asymptotics; damping coefficient},
language = {eng},
number = {5},
pages = {1-8},
publisher = {Université de Nantes},
title = {Asymptotic distribution of eigenfrequencies for damped wave equations},
url = {http://eudml.org/doc/93393},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Sjöstrand, Johannes
TI - Asymptotic distribution of eigenfrequencies for damped wave equations
JO - Journées équations aux dérivées partielles
PY - 2000
PB - Université de Nantes
VL - 36
IS - 5
SP - 1
EP - 8
LA - eng
KW - Birkhoff limits; Weyl asymptotics; damping coefficient
UR - http://eudml.org/doc/93393
ER -

References

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  1. [1] M. Asch, G. Lebeau, The spectrum of the damped wave operator for a bounded domain in R2. Preprint. Zbl1061.35064
  2. [2] P. Freitas, Spectral sequences for quadratic pencils and the inverse problem for the damped wave equation, J. Math. Pures et Appl., 78 (1999), 965-980. Zbl0956.47006MR2000j:47026
  3. [3] I.C. Gohberg, M.G. Krein, Introduction to the theory of non-selfadjoint operators, Amer. Math. Soc., Providence, RI 1969. Zbl0181.13504
  4. [4] G. Lebeau, Equation des ondes amorties, Algebraic and geometric methods in mathematical physics (Kaciveli, 1993), 73-109, Math. Phys. Stud., 19, Kluwer Acad. Publ., Dordrecht, 1996. Zbl0863.58068
  5. [5] A.S. Markus, V.I. Matsaev, Comparison theorems for spectra of linear operators, and spectral asymptotics, Trans. Moscow Math. Soc. 1984(1), 139-187. Russian original in Trudy Moscow. Obshch. 45 (1982), 133-181. Zbl0532.47012MR85b:47002
  6. [6] J. Rauch, M. Taylor, Decay of solutions to nondissipative hyperbolic systems on compact manifolds, Comm. Pure. Appl. Math. 28 (1975), 501-523. Zbl0295.35048MR53 #1044a
  7. [7] J. Sjöstrand, Asymptotic distribution of eigenfrequencies for damped wave equations, Publ. R.I.M.S., to appear. Zbl1213.35331
  8. [8] J. Sjöstrand, Density of resonances for strictly convex analytic obstacles, Can. J. Math., 48(2)(1996), 397-447. Zbl0863.35072MR97j:35117
  9. [9] J. Sjöstrand, A trace formula and review of some estimates for resonances, p.377-437 in Microlocal Analysis and spectral theory, NATO ASI Series C, vol. 490, Kluwer 1997. See also Resoances for bottles and trace formulae, Math. Nachr., to appear. Zbl0877.35090MR99e:47064
  10. [10] J. Sjöstrand, M. Zworski, Asymptotic distribution of resonances for convex obstacles, Acta. Math., 183(2)(2000), 191. Zbl0989.35099

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