Nonlinear evolution PDEs in R + ×C d : existence and uniqueness of solutions, asymptotic and Borel summability properties
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 5, pp. 795-823.
@article{AIHPC_2007__24_5_795_0,
     author = {Costin, O. and Tanveer, S.},
     title = {Nonlinear evolution {PDEs} in ${R}^{+}\times {C}^{d}$ : existence and uniqueness of solutions, asymptotic and {Borel} summability properties},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {795--823},
     publisher = {Elsevier},
     volume = {24},
     number = {5},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.07.002},
     mrnumber = {2348053},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.07.002/}
}
TY  - JOUR
AU  - Costin, O.
AU  - Tanveer, S.
TI  - Nonlinear evolution PDEs in ${R}^{+}\times {C}^{d}$ : existence and uniqueness of solutions, asymptotic and Borel summability properties
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2007
SP  - 795
EP  - 823
VL  - 24
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2006.07.002/
DO  - 10.1016/j.anihpc.2006.07.002
LA  - en
ID  - AIHPC_2007__24_5_795_0
ER  - 
%0 Journal Article
%A Costin, O.
%A Tanveer, S.
%T Nonlinear evolution PDEs in ${R}^{+}\times {C}^{d}$ : existence and uniqueness of solutions, asymptotic and Borel summability properties
%J Annales de l'I.H.P. Analyse non linéaire
%D 2007
%P 795-823
%V 24
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2006.07.002/
%R 10.1016/j.anihpc.2006.07.002
%G en
%F AIHPC_2007__24_5_795_0
Costin, O.; Tanveer, S. Nonlinear evolution PDEs in ${R}^{+}\times {C}^{d}$ : existence and uniqueness of solutions, asymptotic and Borel summability properties. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 5, pp. 795-823. doi : 10.1016/j.anihpc.2006.07.002. http://www.numdam.org/articles/10.1016/j.anihpc.2006.07.002/

[1] Balser W., From Divergent Power Series to Analytic Functions, Springer-Verlag, Berlin, 1994. | MR | Zbl

[2] W. Balser, Multisummability of formal power series solutions of partial differential equations with constant coefficients, preprint. | MR | Zbl

[3] Balser W., Divergent solutions of the heat equation: on an article of Lutz, Miyake and Schäfke, Pacific J. Math. 188 (1) (1999) 53-63. | MR | Zbl

[4] Bender C., Orszag S., Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, 1978, Springer-Verlag, 1999. | MR | Zbl

[5] Costin O., On Borel summation and Stokes phenomena for rank-1 nonlinear systems of ordinary differential equations, Duke Math. J. 93 (2) (1998) 289. | MR | Zbl

[6] Costin O., Costin R.D., On the formation of singularities of solutions of nonlinear differential systems in antistokes directions, Invent. Math. 45 (3) (2001) 425-485. | MR | Zbl

[7] Costin O., Tanveer S., Existence and uniqueness for a class of nonlinear higher-order partial differential equations in the complex plane, Comm. Pure Appl. Math. LIII (2000) 1092-1117. | MR | Zbl

[8] Costin O., Topological construction of transseries and introduction to generalized Borel summability, in: Analyzable Functions and Applications, Contemp. Math., vol. 373, Amer. Math. Soc., Providence, RI, 2005, pp. 137-175. | MR | Zbl

[9] O. Costin, S. Tanveer, Complex singularity analysis for a nonlinear PDE, Comm. PDE, in press.

[10] Écalle J., Bifurcations and Periodic Orbits of Vector Fields, NATO ASI Series, vol. 408, 1993.

[11] Écalle J., Fonctions analysables et preuve constructive de la conjecture de Dulac, Hermann, Paris, 1992. | MR

[12] Lutz D.A., Miyake M., Schäfke R., On the Borel summability of divergent solutions of the heat equation, Nagoya Math. J. 154 (1999) 1. | MR | Zbl

[13] Sammartino M., Caflisch R.E., Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations, Comm. Math. Phys. 192 (1998) 433-461. | Zbl

[14] Sammartino M., Caflisch R.E., Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. II. Construction of the Navier-Stokes solution, Comm. Math. Phys. 192 (1998) 463. | Zbl

[15] Tanveer S., Evolution of Hele-Shaw interface for small surface tension, Philos. Trans. Roy. Soc. London A 343 (1993) 155. | Zbl

[16] Treves F., Basic Linear Partial Differential Equations, Academic Press, 1975. | MR | Zbl

Cité par Sources :