Self-similar solutions of the Laplacian growth problem in the half-plane

D. V. Vasiliev, A. V. Zabrodin

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)23-36
Number of pages14
JournalTheoretical and Mathematical Physics
Issue number1
Publication statusPublished - Jan 2011
Externally publishedYes


  • conformal map
  • harmonic moment
  • integrable system
  • Laplacian growth


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