Free Access
Volume 11, Number 3, July 2005
Page(s) 487 - 507
Published online 15 July 2005
  1. W. Arendt and C.J.K. Batty, Tauberian theorems and stability of one-parameter semigroups. Trans. Am. Math. Soc. 306 (1988) 837–852. [Google Scholar]
  2. H. Brezis, Analyse fonctionnelle. Théorie et applications. Masson, Paris (1983). [Google Scholar]
  3. M. Bruneau, Ph. Herzog, J. Kergomard and J.-D. Polack, General formulation of the dispersion equation in bounded visco-thermal fluid, and application to some simple geometries. Wave Motion 11 (1989) 441–451. [CrossRef] [Google Scholar]
  4. T. Cazenave and A. Haraux, An introduction to semilinear evolution equations. Oxford Lecture Series in Mathematics and its Applications 13 (1998). [Google Scholar]
  5. F. Conrad and M. Pierre, Stabilization of second order evolution equations by unbounded nonlinear feedback. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 11 (1994) 485–515. [Google Scholar]
  6. R.F. Curtain and H. Zwart, An introduction to infinite-dimensional linear systems theory. Texts Appl. Math. 21 (1995). [Google Scholar]
  7. G. Dauphin, D. Heleschewitz and D. Matignon, Extended diffusive representations and application to non-standard oscillators, in Proc. of Math. Theory on Network Systems (MTNS), Perpignan, France (2000). [Google Scholar]
  8. R. Dautray and J.-L. Lions, Mathematical analysis and numerical methods for science and technology, Vol. 5. Springer, New York (1984). [Google Scholar]
  9. Z.E.A. Fellah, C. Depollier and M. Fellah, Direct and inverse scattering problem in porous material having a rigid frame by fractional calculus based method. J. Sound Vibration 244 (2001) 3659–3666. [Google Scholar]
  10. H. Haddar, T. Hélie and D. Matignon, A Webster-Lokshin model for waves with viscothermal losses and impedance boundary conditions: strong solutions, in Proc. of Sixth international conference on mathematical and numerical aspects of wave propagation phenomena, Jyväskylä, Finland (2003) 66–71. [Google Scholar]
  11. Th. Hélie, Unidimensional models of acoustic propagation in axisymmetric waveguides. J. Acoust. Soc. Am. 114 (2003) 2633–2647. [Google Scholar]
  12. A.E. Ingham, On Wiener's method in Tauberian theorems, in Proc. London Math. Soc. II 38 (1935) 458–480. [Google Scholar]
  13. J. Korevaar, On Newman's quick way to the prime number theorem. Math. Intell. 4 (1982) 108–115. [CrossRef] [Google Scholar]
  14. A.A. Lokshin, Wave equation with singular retarded time. Dokl. Akad. Nauk SSSR 240 (1978) 43–46 (in Russian). [MathSciNet] [Google Scholar]
  15. A.A. Lokshin and V.E. Rok, Fundamental solutions of the wave equation with retarded time. Dokl. Akad. Nauk SSSR 239 (1978) 1305–1308 (in Russian). [MathSciNet] [Google Scholar]
  16. Z.-H. Luo, B.-Z. Guo and O. Morgul, Stability and stabilization of infinite dimensional systems and applications. Comm. Control Engrg. Springer-Verlag, New York (1999). [Google Scholar]
  17. Yu.I. Lyubich and V.Q. Phóng, Asymptotic stability of linear differential equations in Banach spaces. Stud. Math. 88 (1988) 37–42. [Google Scholar]
  18. D. Matignon, Stability properties for generalized fractional differential systems. ESAIM: Proc. 5 (1998) 145–158. [CrossRef] [EDP Sciences] [Google Scholar]
  19. G. Montseny, Diffusive representation of pseudo-differential time-operators. ESAIM: Proc. 5 (1998) 159–175. [CrossRef] [EDP Sciences] [Google Scholar]
  20. D.J. Newman, Simple analytic proof of the prime number theorem. Am. Math. Mon. 87 (1980) 693–696. [CrossRef] [Google Scholar]
  21. J.-D. Polack, Time domain solution of Kirchhoff's equation for sound propagation in viscothermal gases: a diffusion process. J. Acoustique 4 (1991) 47–67. [Google Scholar]
  22. O.J. Staffans, Well-posedness and stabilizability of a viscoelastic equation in energy space. Trans. Am. Math. Soc. 345 (1994) 527–575. [CrossRef] [Google Scholar]
  23. O.J. Staffans, Passive and conservative continuous-time impedance and scattering systems. Part I: Well-posed systems. Math. Control Sig. Syst. 15 (2002) 291–315. [CrossRef] [Google Scholar]
  24. G. Weiss, O.J. Staffans and M. Tucsnak, Well-posed linear systems – a survey with emphasis on conservative systems. Internat. J. Appl. Math. Comput. Sci. 11 (2001) 7–33. [Google Scholar]
  25. G. Weiss and M. Tucsnak, How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance. ESAIM: COCV 9 (2003) 247–273. [CrossRef] [EDP Sciences] [Google Scholar]

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