Nonlocal variational problems arising in long wave propagation

Orlando Lopes

ESAIM: Control, Optimisation and Calculus of Variations (2000)

  • Volume: 5, page 501-528
  • ISSN: 1292-8119

How to cite

top

Lopes, Orlando. "Nonlocal variational problems arising in long wave propagation." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 501-528. <http://eudml.org/doc/90580>.

@article{Lopes2000,
author = {Lopes, Orlando},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {stability of traveling waves; constrained variational problems},
language = {eng},
pages = {501-528},
publisher = {EDP Sciences},
title = {Nonlocal variational problems arising in long wave propagation},
url = {http://eudml.org/doc/90580},
volume = {5},
year = {2000},
}

TY - JOUR
AU - Lopes, Orlando
TI - Nonlocal variational problems arising in long wave propagation
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2000
PB - EDP Sciences
VL - 5
SP - 501
EP - 528
LA - eng
KW - stability of traveling waves; constrained variational problems
UR - http://eudml.org/doc/90580
ER -

References

top
  1. [1] R. Adams, Sobolev Spaces. Academic Press ( 1975). Zbl0314.46030MR450957
  2. [2] J. Albert, Concentration-Compactness and stability-wave solutions to nonlocal equations. Contemp. Math. 221, AMS ( 1999) 1-30. Zbl0936.35159MR1647189
  3. [3] J. Albert, J. Bona and D. Henry, Sufficient conditions for stability of solitary-wave solutions of model equations for long waves. Phys. D 24 ( 1987) 343-366. Zbl0634.35079MR887857
  4. [4] J. Albert, J. Bona and J.C. Saut, Model equations for waves in stratified fluids. Proc. Roy. Soc. London Ser. A 453 ( 1997) 1233-1260. Zbl0886.35111MR1455330
  5. [5] J. Bergh and J. Lofstrom, Interpolation Spaces. Springer-Verlag, New-York/Berlin ( 1976). Zbl0344.46071MR482275
  6. [6] P. Blanchard and E. Bruning, Variational Methods in Mathematical Physics. Springer-Verlag ( 1992). Zbl0756.49023MR1230382
  7. [7] H. Brezis and E. Lieb, Minimum Action Solutions of Some Vector Field Equations. Comm. Math. Phys. 96 ( 1984) 97-113. Zbl0579.35025MR765961
  8. [8] A. de Bouard, Stability and instability of some nonlinear dispersive solitary waves in higher dimension. Proc. Roy. Soc. Edinburgh Sect. A 126 ( 1996) 89-112. Zbl0861.35094MR1378834
  9. [9] I. Catto and P.L. Lions, Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories, Part I. Comm. Partial Differential Equations 17 ( 1992) 1051-1110. Zbl0767.35065MR1179279
  10. [10] T. Cazenave and P.L. Lions, Orbital Stability of Standing waves for Some Nonlinear Schrödinger Equations. Comm. Math. Phys. 85 ( 1982) 549-561. Zbl0513.35007MR677997
  11. [11] S. Coleman, V. Glazer and A. Martin, Action Minima among to a class of Euclidean Scalar Field Equations. Comm. Math. Phys. 58 ( 1978) 211-221. MR468913
  12. [12] T. Colin and M. Weinstein, On the ground states of vector nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Phys. Théor. 65 ( 1996) 57-79. Zbl0863.35101MR1407166
  13. [13] G.H. Derrick, Comments on Nonlinear Wave Equations as Models for Elementary Particles. J. Math. Phys. 5, 9 ( 1964) 1252-1254. MR174304
  14. [14] M. Grillakis, J. Shatah and W. Strauss, Stability of Solitary Waves in the Presence of Symmetry I. J. Funct. Anal. 74 ( 1987) 160-197. Zbl0656.35122MR901236
  15. [15] L. Hormander, Estimates for translation invariant operators in Lp spaces. Acta Math. 104 ( 1960) 93-140. Zbl0093.11402MR121655
  16. [16] O. Kavian, Introduction à la théorie des points critiques et applications aux problèmes elliptiques. Springer, Heidelberg ( 1993). Zbl0797.58005MR1276944
  17. [17] P. Lax, Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math. 21 ( 1968) 467-490. Zbl0162.41103MR235310
  18. [18] S. Levandosky, Stability and instability of fourth-order solitary waves. J. Dynam. Differential Equations 10 ( 1998) 151-188. Zbl0893.35079
  19. [19] E. Lieb, Existence and uniqueness of minimizing solutions of Choquard's nonlinear equation. Stud. Appl. Math. 57 ( 1977) 93-105. Zbl0369.35022
  20. [20] P.L. Lions, The Concentration-Compactness Principle in the Calculus of Variations. Ann. Inst. H. Poincaré Anal. Non Linéaire 1 ( 1984) Part I 109-145, Part II 223-283. Zbl0704.49004
  21. [21] P.L. Lions, Solutions of Hartree-Fock Equations for Coulomb Systems. Comm. Math. Phys. 109 ( 1987) 33-97. Zbl0618.35111
  22. [22] O. Lopes, Radial symmetry of minimizers for some translation and rotation invariant functionals. J. Differential Equations 124 ( 1996) 378-388. Zbl0842.49004
  23. [23] O. Lopes, Sufficient conditions for minima of some translation invariant functionals. Differential Integral Equations 10 ( 1997) 231-244. Zbl0891.49001MR1424809
  24. [24] O. Lopes, A Constrained Minimization Problem with Integrals on the Entire Space. Bol. Soc. Brasil Mat. (N.S.) 25 ( 1994) 77-92. Zbl0805.49005MR1274763
  25. [25] O. Lopes, Variational Systems Defined by Improper Integrals, edited by L. Magalhaes et al., International Conference on Differential Equations. World Scientific ( 1998) 137-153. Zbl0961.35034MR1639339
  26. [26] O. Lopes, Variational problems defined by integrals on the entire space and periodic coefficients. Comm. Appl. Nonlinear Anal. 5 ( 1998) 87-120. Zbl1108.49300MR1621231
  27. [27] J. Maddocks and R. Sachs, On the stability of KdV multi-solitons. Comm. Pure. Appl. Math. 46 ( 1993) 867-902. Zbl0795.35107MR1220540
  28. [28] J.C. Saut, Sur quelques généralizations de l'équation de Korteweg-de Vries. J. Math. Pure Appl. (9) 58 ( 1979) 21-61. Zbl0449.35083MR533234
  29. [29] H. Triebel, Interpolation Theory, Functions Spaces, Differential Operators. North-Holland, Amsterdam ( 1978). Zbl0387.46032MR503903
  30. [30] M. Weinstein, Liapunov Stability of Ground States of Nonlinear Dispersive Evolution Equations. Comm. Pure Appl. Math. 39 ( 1986) 51-68. Zbl0594.35005MR820338
  31. [31] M. Weinstein, Existence and dynamic stability of solitary wave solution of equations arising in long wave propagation. Comm. Partial Differential Equations 12 ( 1987) 1133-1173. Zbl0657.73040MR886343

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.