Pole solutions in the case of problems of flame front propagation and Saffman-Teylor "finger" formation without surface tension: open problems and possible ways of their solutions

2003/06/18 by Oleg Kupervasser, Kupervasser, Oleg
Engineering · Physics and Astronomy · #FOS: Physical sciences #Material Science and Thermodynamics #Pattern Formation and Solitons (nlin.PS) #nlin.PS

paper · pdf · doi:10.48550/arxiv.nlin/0306038

3 pages

arxiv created 2003/06/18 · openalex publication_date 2003/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some physical problems as flame front propagation or Laplacian growth without surface tension have nice analytical solutions which replace its complex integro-differential motion equations by simple differential equations of poles motion in a complex plane. Investigation of these equation was the main topic of Kupervasser Oleg Ph.D. Thesis[7]. Some very interesting open problems were hanged up there. Here we give these open problems and possible ways of their solutions.

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