Elastic wave propagation in fluid-saturated porous media. Part I. The existence and uniqueness theorems

Juan Enrique Santos

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1986)

  • Volume: 20, Issue: 1, page 113-128
  • ISSN: 0764-583X

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Santos, Juan Enrique. "Elastic wave propagation in fluid-saturated porous media. Part I. The existence and uniqueness theorems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 20.1 (1986): 113-128. <http://eudml.org/doc/193465>.

@article{Santos1986,
author = {Santos, Juan Enrique},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Biot's dynamic equations; elastic wave propagation; compressible viscous fluid; Galerkin method},
language = {eng},
number = {1},
pages = {113-128},
publisher = {Dunod},
title = {Elastic wave propagation in fluid-saturated porous media. Part I. The existence and uniqueness theorems},
url = {http://eudml.org/doc/193465},
volume = {20},
year = {1986},
}

TY - JOUR
AU - Santos, Juan Enrique
TI - Elastic wave propagation in fluid-saturated porous media. Part I. The existence and uniqueness theorems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1986
PB - Dunod
VL - 20
IS - 1
SP - 113
EP - 128
LA - eng
KW - Biot's dynamic equations; elastic wave propagation; compressible viscous fluid; Galerkin method
UR - http://eudml.org/doc/193465
ER -

References

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  1. [1] M.A. BIOT, General Theory of Three-Dimensional Consolidation, Journal of Applied Physics, Vol. 12 (1941), pp. 155-165. Zbl67.0837.01JFM67.0837.01
  2. [2] M. A. BIOT, Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range, Journal of the Acoustical Society of America, Vol. 28, Number 2 (1965), pp. 168-178. MR134056
  3. [3] M. A. BIOT and D. G. WILLIS, The Elastic Coefficient of the Theory of Consolidation, Journal of Applied Mechanics, Vol. 24, Trans. Asme, Vol. 79 (1957), pp. 594-601. MR92472
  4. [4] G. DUVAUT and J. L. LIONS, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976. Zbl0331.35002MR521262
  5. [5] I. FATT, The Biot-Willis Elastic Coefficients for a Sandstone, Journal of Applied Mechanics, Vol. 26 (1959), pp. 296-297. 
  6. [6] G. FICHERA, Existence Theorems in Elasticity-Boundary Value Problems of Elasticity with Unilateral Constrains, Encyclopedia of Physics, S. Flüge, Ed., Vol. VI a/2 : Mechanics of Solids II, C. Truesdell, Ed., Springer-Verlag, Berlin, 1972, pp. 347-424. 
  7. [7] V. GIRAULT and P. A. RAVIART, Finite Element Approximation of the Navier-Stokes Equations, Springer-Verlag, Berlin, 1981. Zbl0441.65081MR548867
  8. [8] J. L. LIONS, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
  9. [9] J. A. NITSCHE, On Korn's Second Inequality, preprint, Institute für Angenwandte Mathematik, Albert Ludwig Universitat, Herman-Herder Str. 10, 7800, Freiburg i, Br., West Germany. Zbl0467.35019

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