The limiting amplitude principle applied to the motion of floating bodies

Martine Vullierme-Ledard

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1987)

  • Volume: 21, Issue: 1, page 125-170
  • ISSN: 0764-583X

How to cite

top

Vullierme-Ledard, Martine. "The limiting amplitude principle applied to the motion of floating bodies." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.1 (1987): 125-170. <http://eudml.org/doc/193494>.

@article{Vullierme1987,
author = {Vullierme-Ledard, Martine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {rigid body; ocean of infinite depth; time-harmonic motions of small amplitude; spectral analysis techniques; transient motion; limiting amplitude principle},
language = {eng},
number = {1},
pages = {125-170},
publisher = {Dunod},
title = {The limiting amplitude principle applied to the motion of floating bodies},
url = {http://eudml.org/doc/193494},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Vullierme-Ledard, Martine
TI - The limiting amplitude principle applied to the motion of floating bodies
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 1
SP - 125
EP - 170
LA - eng
KW - rigid body; ocean of infinite depth; time-harmonic motions of small amplitude; spectral analysis techniques; transient motion; limiting amplitude principle
UR - http://eudml.org/doc/193494
ER -

References

top
  1. [1] F. JOHN, On the Motion of Floating Bodies, II, Comm. Pure Appl. Math., Vol. 3, 1950, pp. 45-101. MR37118
  2. [2] O. A. LADYZENSKAYA, On the Principle of Limiting Amplitude, Uspehi Mat Nauk 12, # 3 (75), 1957, pp. 161-164. MR90401
  3. [3] E. SANCHEZ-PALENCIA, Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics # 127, Springer, Berlin, 1980. Zbl0432.70002MR578345
  4. [4] C. S. MORAWETZ, The Limiting Amplitude Principle for Arbitrary Finite Bodies, Comm. Pure Appl. Math, Vol. 18, 1965, pp. 183-189. Zbl0161.08201MR190516
  5. [5] R. BUCHAL, The approach to Steady-State of Solutions of Exterior Boundary Value Problems for the Wave Equation, J. Math. Mech, Vol. 12, # 2, 1963, pp.225-234. Zbl0108.28302MR145217
  6. [6] C. S. MORAWETZ, The Limiting Amplitude Principle, Comm. Pure Appl. Math., Vol. 15, 1962, pp. 349-362. Zbl0196.41202MR151712
  7. [7] P. D. LAX& R. S. PHILLIPS, Scattering Theory, Academic Press, New York, 1967. Zbl0186.16301MR217440
  8. [8] D. M. EIDUS, On the Principle of Limiting Absorption, Mat. Sb. N.S. 57, 99, 1962, pp. 13-44. Zbl0149.30602MR145187
  9. [9] J. THOMAS BEALE, Eigenfunction Expansions for Objects Floating in an Open Sea, Comm. Pure Appl. Math., Vol. 30, # 3, 1977, pp. 283-313. Zbl0336.76004MR670432
  10. [10] B. HANOUZET, Espace de Sobolev avec Poids, Application au Problème de Dirichlet dans un Demi-Espace, Rend, della Sem. Math., Univ. di Padova, vol. 46, 1971, pp. 227-272. Zbl0247.35041MR310417
  11. [11] K. HAMDACHE, Forward Speed Motion of a Submerged Body, the Cauchy Problem, Math. Meth. in the Appl. Sci., Vol. 6, 1984, pp. 371-392. Zbl0568.35059MR761499
  12. [12] J. C. NEDELEC, Approximation des Equations Intégrales en Mécanique et en Physique, Cours de l'Ecole d'Eté d'Analyse Numérique, EDF-IRIA-CEA, juin 1977. 
  13. [13] M. LENOIR& D. MARTIN, An Application of the Limiting Absorption Principle to the Motion of Floating Bodies, J. Math. Anal. Appl., Vol. 79, 1981, pp. 370-383. Zbl0464.76013MR606488
  14. [14] M. VULLIERME-LEDARD, Vibrations Engendrées par les Oscillations Forcées d'un Corps Rigide Immergé dans un Fluide Incompressible présentant une Surface Libre, C.R. Acad. Sc., t. 296, Serie I, 1983, pp. 611-614. Zbl0524.76024MR705174
  15. [15] M. VULLIERME-LEDARD, Asymptotic Study of the Vibration Problem for an Elastic Body Deeply Immersed in an Incompressible Fluid, RAIRO, Mathematical Model-ling and Numerical Analysis, Vol. 19, # 1, 1985, pp. 145-170. Zbl0584.73059MR813692
  16. [16] T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966. Zbl0148.12601MR203473
  17. [17] J. DIEUDONNÉ, Eléments d'analyse, tome 2, Gauthier-Villars, Paris, 1969. Zbl0189.05502
  18. [18] I. SEGAL & H. KUNZE, Integrals and operators, Springer, 1978. Zbl0373.28001MR486380
  19. [19] J. NECAS, Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, 1967. MR227584
  20. [20] F. RELLICH, Uber das asymptotische Verhalten der Losungen von Δ u + λ u = 0 in unendlichen Gebieten, Uber. Deutschen Math. Verein., Vol. 53, 1943, pp. 57-64. Zbl0028.16401MR17816

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.