no. 6
Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 6, pp. 783-797 
@article{AIHPC_2005__22_6_783_0,
     author = {Bona, Jerry L. and Gruji\'c, Zoran and Kalisch, Henrik},
     title = {Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized {KdV} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {783--797},
     year = {2005},
     publisher = {Elsevier},
     volume = {22},
     number = {6},
     doi = {10.1016/j.anihpc.2004.12.004},
     mrnumber = {2172859},
     zbl = {1095.35039},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2004.12.004/}
}
TY  - JOUR
AU  - Bona, Jerry L.
AU  - Grujić, Zoran
AU  - Kalisch, Henrik
TI  - Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2005
SP  - 783
EP  - 797
VL  - 22
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2004.12.004/
DO  - 10.1016/j.anihpc.2004.12.004
LA  - en
ID  - AIHPC_2005__22_6_783_0
ER  - 
%0 Journal Article
%A Bona, Jerry L.
%A Grujić, Zoran
%A Kalisch, Henrik
%T Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2005
%P 783-797
%V 22
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2004.12.004/
%R 10.1016/j.anihpc.2004.12.004
%G en
%F AIHPC_2005__22_6_783_0
Bona, Jerry L.; Grujić, Zoran; Kalisch, Henrik. Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 6, pp. 783-797. doi: 10.1016/j.anihpc.2004.12.004

[1] Bona J.L., Dougalis V.A., Karakashian O.A., Mckinney W.R., Conservative high-order numerical schemes for the generalized Korteweg-de Vries equation, Philos. Trans. Roy. Soc. London Ser. A 351 (1995) 107-164. | Zbl | MR

[2] Bona J.L., Dougalis V.A., Karakashian O.A., Mckinney W.R., Numerical simulation of singular solutions of the generalized Korteweg-de Vries equation, in: Dias F., Ghidaglia J.-M., Saut J.-C. (Eds.), Contemp. Math., vol. 200, Amer. Math. Soc., Providence, RI, 1996, pp. 17-29. | Zbl | MR

[3] Bona J.L., Grujić Z., Spatial analyticity for nonlinear waves, Math. Models Methods Appl. Sci. 13 (2003) 1-15. | MR | Zbl

[4] Bona J.L., Weissler F.B., Similarity solutions of the generalized Korteweg-de Vries equation, Math. Proc. Cambridge Philos. Soc. 127 (1999) 323-351. | Zbl | MR

[5] Bona J.L., Weissler F.B., Blow-up of spatially periodic complex-valued solutions of nonlinear dispersive equations, Indiana Univ. Math. J. 50 (2001) 759-782. | MR | Zbl

[6] Bourgain J., Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Geom. Funct. Anal. 3 (1993) 107-156, 209-262. | Zbl | MR | EuDML

[7] De Bouard A., Hayashi N., Kato K., Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1995) 673-715. | Zbl | MR | Numdam | EuDML

[8] Foias C., Temam R., Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal. 87 (1989) 359-369. | Zbl | MR

[9] Ginibre J., Tsutsumi Y., Velo G., On the Cauchy problem for the Zakharov system, J. Funct. Anal. 151 (1997) 384-436. | Zbl | MR

[10] Grujić Z., Kalisch H., Local well-posedness of the generalized Korteweg-de Vries equation in spaces of analytic functions, Differential Integral Equations 15 (2002) 1325-1334. | Zbl | MR

[11] Hayashi N., Analyticity of solutions of the Korteweg-de Vries equation, SIAM J. Math. Anal. 22 (1991) 1738-1743. | Zbl | MR

[12] Hayashi N., Solutions of the (generalized) Korteweg-de Vries equation in the Bergman and Szegö spaces on a sector, Duke Math. J. 62 (1991) 575-591. | Zbl | MR

[13] Kato T., Quasilinear equations of evolution with applications to partial differential equations, in: Lecture Notes in Math., vol. 448, Springer-Verlag, 1975, pp. 25-70. | Zbl | MR

[14] Kato T., On the Korteweg-deVries equation, Manuscripta Math. 28 (1979) 89-99. | Zbl | MR

[15] Kato T., Masuda K., Nonlinear evolution equations and analyticity I, Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 455-467. | Zbl | MR | Numdam

[16] Kato K., Ogawa T., Analyticity and smoothing effect for the Korteweg-de Vries equation with a single point singularity, Math. Ann. 316 (2000) 577-608. | Zbl | MR

[17] Kenig C.E., Ponce G., Vega L., Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991) 33-69. | Zbl | MR

[18] Kenig C.E., Ponce G., Vega L., On the Cauchy problem for the Korteweg-deVries equation in Sobolev spaces of negative indices, Duke Math. J. 71 (1993) 1-20. | Zbl | MR

[19] Martel Y., Merle F., Blow up in finite time and dynamics of blow up solutions for the L 2 -critical generalized KdV equation, J. Amer. Math. Soc. 15 (2002) 617-664. | Zbl | MR

[20] Staffilani G., On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations, Duke Math. J. 86 (1997) 109-142. | Zbl | MR

Cité par Sources :