@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}, publisher = {Elsevier}, volume = {22}, number = {6}, year = {2005}, doi = {10.1016/j.anihpc.2004.12.004}, mrnumber = {2172859}, zbl = {1095.35039}, language = {en}, url = {http://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 - http://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 http://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. http://www.numdam.org/articles/10.1016/j.anihpc.2004.12.004/
[1] Conservative high-order numerical schemes for the generalized Korteweg-de Vries equation, Philos. Trans. Roy. Soc. London Ser. A 351 (1995) 107-164. | MR | Zbl
, , , ,[2] Numerical simulation of singular solutions of the generalized Korteweg-de Vries equation, in: , , (Eds.), Contemp. Math., vol. 200, Amer. Math. Soc., Providence, RI, 1996, pp. 17-29. | MR | Zbl
, , , ,[3] Spatial analyticity for nonlinear waves, Math. Models Methods Appl. Sci. 13 (2003) 1-15. | MR | Zbl
, ,[4] Similarity solutions of the generalized Korteweg-de Vries equation, Math. Proc. Cambridge Philos. Soc. 127 (1999) 323-351. | MR | Zbl
, ,[5] Blow-up of spatially periodic complex-valued solutions of nonlinear dispersive equations, Indiana Univ. Math. J. 50 (2001) 759-782. | MR | Zbl
, ,[6] Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Geom. Funct. Anal. 3 (1993) 107-156, 209-262. | EuDML | MR | Zbl
,[7] 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. | EuDML | Numdam | MR | Zbl
, , ,[8] Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal. 87 (1989) 359-369. | MR | Zbl
, ,[9] On the Cauchy problem for the Zakharov system, J. Funct. Anal. 151 (1997) 384-436. | MR | Zbl
, , ,[10] Local well-posedness of the generalized Korteweg-de Vries equation in spaces of analytic functions, Differential Integral Equations 15 (2002) 1325-1334. | MR | Zbl
, ,[11] Analyticity of solutions of the Korteweg-de Vries equation, SIAM J. Math. Anal. 22 (1991) 1738-1743. | MR | Zbl
,[12] Solutions of the (generalized) Korteweg-de Vries equation in the Bergman and Szegö spaces on a sector, Duke Math. J. 62 (1991) 575-591. | MR | Zbl
,[13] Quasilinear equations of evolution with applications to partial differential equations, in: Lecture Notes in Math., vol. 448, Springer-Verlag, 1975, pp. 25-70. | MR | Zbl
,[14] On the Korteweg-deVries equation, Manuscripta Math. 28 (1979) 89-99. | MR | Zbl
,[15] Nonlinear evolution equations and analyticity I, Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 455-467. | Numdam | MR | Zbl
, ,[16] Analyticity and smoothing effect for the Korteweg-de Vries equation with a single point singularity, Math. Ann. 316 (2000) 577-608. | MR | Zbl
, ,[17] Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991) 33-69. | MR | Zbl
, , ,[18] On the Cauchy problem for the Korteweg-deVries equation in Sobolev spaces of negative indices, Duke Math. J. 71 (1993) 1-20. | MR | Zbl
, , ,[19] Blow up in finite time and dynamics of blow up solutions for the -critical generalized KdV equation, J. Amer. Math. Soc. 15 (2002) 617-664. | MR | Zbl
, ,[20] On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations, Duke Math. J. 86 (1997) 109-142. | MR | Zbl
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