Geodesic
Self-similar solutions of the~Laplacian growth problem in the~half-plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 28-43

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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
Mots-clés : conformal map, harmonic moment. 
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     author = {D. V. Vasiliev and A. V. Zabrodin},
     title = {Self-similar solutions of {the~Laplacian} growth problem in the~half-plane},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a1/}
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D. V. Vasiliev; A. V. Zabrodin. Self-similar solutions of the~Laplacian growth problem in the~half-plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 28-43. http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a1/