@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},
volume = {24},
year = {2007},
pages = {795-823},
doi = {10.1016/j.anihpc.2006.07.002},
mrnumber = {2348053},
zbl = {pre05228823},
language = {en},
url = {http://dml.mathdoc.fr/item/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) pp. 795-823. doi : 10.1016/j.anihpc.2006.07.002. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_5_795_0/
[1] , From Divergent Power Series to Analytic Functions, Springer-Verlag, Berlin, 1994. | MR 1317343 | Zbl 0810.34046
[2] W. Balser, Multisummability of formal power series solutions of partial differential equations with constant coefficients, preprint. | MR 2057538 | Zbl 1052.35048
[3] , Divergent solutions of the heat equation: on an article of Lutz, Miyake and Schäfke, Pacific J. Math. 188 (1) (1999) 53-63. | MR 1680415 | Zbl 0960.35045
[4] , , Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, 1978, Springer-Verlag, 1999. | MR 538168 | Zbl 0417.34001
[5] , On Borel summation and Stokes phenomena for rank-1 nonlinear systems of ordinary differential equations, Duke Math. J. 93 (2) (1998) 289. | MR 1625999 | Zbl 0948.34068
[6] , , On the formation of singularities of solutions of nonlinear differential systems in antistokes directions, Invent. Math. 45 (3) (2001) 425-485. | MR 1856397 | Zbl 1034.34102
[7] , , 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 1761410 | Zbl 1069.35003
[8] , 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 2130829 | Zbl 1072.40004
[9] O. Costin, S. Tanveer, Complex singularity analysis for a nonlinear PDE, Comm. PDE, in press. | Zbl pre05040856
[10] , Bifurcations and Periodic Orbits of Vector Fields, NATO ASI Series, vol. 408, 1993.
[11] , Fonctions analysables et preuve constructive de la conjecture de Dulac, Hermann, Paris, 1992. | MR 1399559
[12] , , , On the Borel summability of divergent solutions of the heat equation, Nagoya Math. J. 154 (1999) 1. | MR 1689170 | Zbl 0958.35061
[13] , , 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 0913.35102
[14] , , 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 0913.35103
[15] , Evolution of Hele-Shaw interface for small surface tension, Philos. Trans. Roy. Soc. London A 343 (1993) 155. | Zbl 0778.76029
[16] , Basic Linear Partial Differential Equations, Academic Press, 1975. | MR 447753 | Zbl 0305.35001