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Self-similar solutions to the generalized deterministic KPZ equation |
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| Authors: | Mohammed GUEDDA Robert KERSNER |
| Affiliation: | (1) Lamfa, CNRS FRE 2270, Université de Picardie Jules Verne, Faculté de Mathématiques et d'Informatique, 33, rue Saint-Leu, F-80039 Amiens, France, e-mail: mohamed.guedda@u-picardie.fr, FR;(2) Computer and Automation Research Institute, Hungarian Academy of Sciences, P.O. Box 63, H-1518 Budapest, Hungary, e-mail: kersner@sztaki.hu, HU |
| Abstract: | Geometric properties of shape functions of self-similar solution to the equation are studied, and q are positive numbers. These shapes-the solutions of the corresponding nonlinear ODE-are of very different nature. The properties usually depend on three critical values of q (1, 3/2 and 2). For the range 1<q<2 the dependence of is more remarkable, for example there is no global existence in general. |
| Keywords: | 2000 Mathematics Subject Classification: 35K55 35K65.?: Surface growth KPZ equation self-similar solutions global existence. |
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