This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
L. Abdelouhab, J. Bona, M. Felland and J. Saut, “Non-local models for nonlinear, dispersive waves”, preprint 1989. To appear in Physica D.
E. A. Alarcon, “The Cauchy problem for the generalised Ott-Sudan equation”, Doctoral Thesis, IMPA, 1990.
P. Butzer and R. Nessel, “Fourier Analysis and Approximation vol. 1. One Dimensional Theory” Birkhauser Verlag, (1971).
J. Bona and J. Saut, “Singularités dispersives de solutions d'equations de type Korteweg-de Vries”, C.R. Acad. Sc. Paris, t. 303, Série I, no.4, (1986), 101–103.
J. Bona and R. Scott, “Solutions of the Korteweg-de Vries equation in fractional order Sobolev spaces”, Duke Mathematical Journal, vol. 43, no.1, (1976), 87–99.
J. Bona and R. Smith, “The initial value problem for the Korteweg-de Vries equation”, Philos. Trans. Roy. Soc. London, Ser. A 278, (1975), 555–601.
K. M. Case, “Benjamin-Ono related equations and their solutions”, Proc. Nat. Acad. Sci. U.S.A., vol. 76, no.1, (1979), 1–3.
R. Coiffman, A. McIntosh and Y. Meyer, “L'integrale de Cauchy sur les courbes lipschtziennes”, Ann. of Math, 116, (1982), 361–387.
Dan Henry “Geometric theory of semilinear parabolic equations”, Lecture notes in Mathematics 840, Springer Verlag, (1981).
J. Hounie, “Remarks on the Benjamin-Ono equation”, private communication, (1989).
R. J. Iorio, Jr., “On the Cauchy problem for the Benjamin-Ono equation” Commun. in Partial Differential Equations, 11(10), (1986), 1031–1081.
R. J. Iório, Jr., “The Benjamin-Ono equation in weighted Sobolev spaces”, preprint IMPA, (1989). Submitted for publication in Journal of Mathematical Analysis and Applications.
R. J. Iório, Jr., “On the relationship between differentiability and spacial decay satisfied by the solutions of certain non-linear evolution equations”, in preparation.
T. Kato, “On the Cauchy problem for the (generalized) Korteweg-de Vries equations”, Studies in Applied Mathematics, Advances in Mathematics Supplementary Studies, vol. 8, Academic Press, (1983), 93–128.
T. Kato, “Weak solutions of infinite-dimensional Hamiltonian systems”, preprint U. C. Berkeley, (1989).
T. Kato, “Linear evolution equations of “hyperbolic” type, II”, J. Math. Soc. Japan, vol. 25, no.4, (1973), 648–666.
T. Kato, “Quasi-linear equations of evolution with application to partial differential equations”, Spectral Theory and Differential Equations, Lecture Notes in Mathematics, 448, Springer Verlag, (1975), 25–70.
T. Kato, “Linear and quasi-linear equations of evolution of hyperbolic type”, Hyperbolicity, C.I.M.E. II CICLO, (1976), 125–191.
T. Kato, “Non-linear equations of evolution in Banach spaces”, Proc. Sympos. Pure Math., vol. 45, Part 2, A.M.S., (1986), 9–23.
T. Kato and H. Fujita, “On the non-stationary Navier-Stokes system”, Rend. Sem. Mat. Univ. Padova, vol. 32, (1962), 243–260.
S. Kruzhkov and A. Faminskii, “Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation”, Math. USSR Sbornik, vol. 48, no.2, (1984), 391–421.
P. Lax, “A Hamiltonian approach to the KdV and other equations”, Nonlinear Evolution Equations, Ed. M. G. Crandall, Academic Press, (1978).
H. Ono, “Algebraic solitary waves in stratified fluids”, J. Phys. Soc. Japan, vol. 39, no.4, (1975), 1082–1091.
G. Ponce, “Regularity of solutions to nonlinear dispersive equations”, preprint U. of Chicago, (1987).
G. Ponce, “Smoothing properties of solutions to the Benjamin-Ono equation”, preprint, U. of Chicago, (1988).
M. Reed and B. Simon, “Methods of Modern Mathematical Physics”, vol. I and II, Academic Press, (1972, 1975).
A. Torchinsky, “Real variable methods in harmonic analysis”, Academic Press (1986).
M. Tsutsumi, “Weighted Sobolev spaces and rapidly decreasing solutions of some nonlinear dispersive wave equations”, J. Diff. Equations 42, (1981), 260–281.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag
About this paper
Cite this paper
Iório, R.J. (1990). KDV, BO and friends in weighted Sobolev spaces. In: Fujita, H., Ikebe, T., Kuroda, S.T. (eds) Functional-Analytic Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084901
Download citation
DOI: https://doi.org/10.1007/BFb0084901
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53393-1
Online ISBN: 978-3-540-46818-9
eBook Packages: Springer Book Archive