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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 166, Number 1, Pages 28–43
DOI: https://doi.org/10.4213/tmf6593 (Mi tmf6593) 		 
Self-similar solutions of the Laplacian growth problem in the half-plane

D. V. Vasilieva, A. V. Zabrodinab

a Institute for Theoretical and Experimental Physics, Moscow, Russia
b Emanuel Institute of Biochemical Physics, RAS, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf6593
Abstract: We investigate a version of the Laplacian growth problem with zero surface tension in the upper half-plane. Using the method of time-dependent conformal maps, we find families of self-similar exact solutions that are expressible in terms of the hypergeometric function.
Keywords: Laplacian growth, integrable system, conformal map, harmonic moment.
Received: 24.05.2010
English version:
Theoretical and Mathematical Physics, 2011, Volume 166, Issue 1, Pages 23–36
DOI: https://doi.org/10.1007/s11232-011-0002-5
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: D. V. Vasiliev, A. V. Zabrodin, “Self-similar solutions of the Laplacian growth problem in the half-plane”, TMF, 166:1 (2011), 28–43; Theoret. and Math. Phys., 166:1 (2011), 23–36
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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