On the linear damped wave equation

Journal of Differential Equations

Volumn 134, Issue 1, 1997, Pages 26-45

  López Gómez, Julián ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031562015     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.3209     Document Type: Article

References (13)

1. 1. C. Bardos, G. Lebeau, and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM J. Control Optim. 30 (1992), 1024-1065.
2. 2. S. Cox and E. Zuazua, The rate at which energy decays in a damped string, Comm. Partial Differential Equations 19 (1994), 213-243.
3. 3. C. M. Dafermos, Asymptotic behavior of solutions of evolution equations, in "Nonlinear Evolution Equations" (M. G. Crandall, Ed.), pp. 103-12, Academic Press, New York, 1978.
4. 4. C. Faber, Beweis das unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die Kreisförmige den tiefsten Grundton gibt, Sitzungsber. Bayer. Akad. der Wiss. Math. Phys. (1923), 169-172.
5. 5. P. Freitas, On some eigenvalue problems related to the wave equation with indefinite damping, J. Differential Equations 127 (1996), 320-335.
6. 6. J. E. Furter and J. López-Gómez, Diffusion mediated permanence problem for an heterogeneous Lotka-Volterra competition model, Proc. Roy. Soc. Edinburgh, in press.
7. 7. A. Haraux, Stabilization of trajectories for some weakly damped hyperbolic equations, J. Differential Equations 59 (1985), 145-154.
8. 8. P. Hess, Periodic-parabolic boundary value problems and positivity, Pitman Research Notes in Mathematics, Vol. 247, 1991.
9. 9. E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises, Math. Annal. 91 (1925), 97-100.
10. 10. G. Lebeau, Équations des ondes amorties, Preprint Université Paris-Sud, Orsay, 1994.
11. 11. J. López-Gómez, On linear weighted boundary value problems, in "Partial Differential Equations: Models in Physics and Biology" (G. Lumer, S. Nicaise, and B. W. Shulze, Eds.), pp. 188-203, Akademie Verlag, Berlin, 1994.
12. 12. J. López-Gómez, The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems, J. Differential Equations 127 (1996), 263-294.
13. 13. E. Zuazua, Exponential decay for the semilinear wave equation with locally distributed damping, Comm. Partial Differential Equations 15 (1990), 205-235.