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
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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