Blow up in finite time and dynamics of blow up solutions for the $L^2$–critical generalized KdV equation
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- by Yvan Martel and Frank Merle
- J. Amer. Math. Soc. 15 (2002), 617-664
- DOI: https://doi.org/10.1090/S0894-0347-02-00392-2
- Published electronically: March 8, 2002
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Abstract:
In this paper, we describe the dynamics of blow up solutions for the critical generalized KdV equation such that the initial data is close to the soliton in $L^2$ and has decay in $L^2$ at the right. In particular, we prove that blow up occurs in finite time, and we obtain an upper bound on the blow up rate.References
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Bibliographic Information
- Yvan Martel
- Affiliation: Département de Mathématiques, Université de Cergy–Pontoise, 2, av. A. Chauvin, 95302 Cergy Pontoise, France
- MR Author ID: 367956
- Email: Yvan.Martel@math.u-cergy.fr
- Frank Merle
- Affiliation: Département de Mathématiques, Université de Cergy–Pontoise, 2, av. A. Chauvin, 95302 Cergy Pontoise, France – and – Institut Universitaire de France
- MR Author ID: 123710
- Email: Frank.Merle@math.u-cergy.fr
- Received by editor(s): March 15, 2001
- Published electronically: March 8, 2002
- © Copyright 2002 American Mathematical Society
- Journal: J. Amer. Math. Soc. 15 (2002), 617-664
- MSC (1991): Primary 35Q53; Secondary 35B05, 35Q51
- DOI: https://doi.org/10.1090/S0894-0347-02-00392-2
- MathSciNet review: 1896235