Uniform estimates for a class of evolution equations

Matania Ben-Artzi; François Trèves

Journées équations aux dérivées partielles (1992)

  • page 1-12
  • ISSN: 0752-0360

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Ben-Artzi, Matania, and Trèves, François. "Uniform estimates for a class of evolution equations." Journées équations aux dérivées partielles (1992): 1-12. <http://eudml.org/doc/93251>.

@article{Ben1992,
author = {Ben-Artzi, Matania, Trèves, François},
journal = {Journées équations aux dérivées partielles},
keywords = {generalized Schrödinger equations; Airy type equations; estimates; oscillatory integral},
language = {eng},
pages = {1-12},
publisher = {Ecole polytechnique},
title = {Uniform estimates for a class of evolution equations},
url = {http://eudml.org/doc/93251},
year = {1992},
}

TY - JOUR
AU - Ben-Artzi, Matania
AU - Trèves, François
TI - Uniform estimates for a class of evolution equations
JO - Journées équations aux dérivées partielles
PY - 1992
PB - Ecole polytechnique
SP - 1
EP - 12
LA - eng
KW - generalized Schrödinger equations; Airy type equations; estimates; oscillatory integral
UR - http://eudml.org/doc/93251
ER -

References

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  2. Ben-Artzi, M. and Klainerman, S. — Decay and regularity for the Schrödinger equation, J. d'Analyse Math. (1992), to appear. Zbl0802.35057
  3. Constantin, P. and Saut, J. C. — Local smoothing properties for dispersive equations, J. Amer. Math. Soc. 1 (1988), 413-439. Zbl0667.35061MR89d:35150
  4. Journé, J. L., Soffer, A. and Sogge, C. D. — Decay estimates for Schrödinger operators, Comm. Pure and Applied Math. (1992), to appear. Zbl0743.35008
  5. Kato, T. — Perturbation Theory for Linear Operators, Springer 1976. Zbl0342.47009MR53 #11389
  6. Kato, T. — Nonlinear Schrödinger equations, in “Schrödinger Operators”, H. Holden and A. Jensen editors, Springer Lecture Notes in Physics ͅ, 1989. Zbl0698.35131
  7. Kenig, C. E., Ponce, G. and Vega, L. — Oscillatory integrals and regularity of dispersive equations, Indiana Univ. J. 40 (1991), 33-69. Zbl0738.35022MR92d:35081
  8. Phong, D. H. and Stein, E. M. — Oscillatory integrals with polynomial phases, (1991), preprint. Zbl0829.42014
  9. Sidi, A., Sulem C. and Sulem, P. L., On the long time behaviour of a generalized KdV equation, Acta Applicandae Math. 7 (1986), 35-47. Zbl0625.35072MR87k:35038
  10. Strichartz, R. — Restriction of Fourier Transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705-714. Zbl0372.35001MR58 #23577
  11. Strichartz, R. — Asymptotic behavior of waves, J. Functional Analysis 40 (1981), 341-357. Zbl0484.35070MR82j:35020
  12. Tomas, P. — Arestriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975), 447-478. Zbl0298.42011MR50 #10681
  13. Tsutsumi, Y. — L2-solutions for nonlinear Schrödinger equations and nonlinear groups, Funkcial. Ekvac. 30 (1987), 115-125. Zbl0638.35021MR89c:35143
  14. Tsutsumi, Y. — Glocal strong solutions for nonlinear Schrödinger equations, Nonlinear Anal. 11 (1987), 1143-1154. Zbl0657.35032MR88m:35144

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