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On the dynamics of roots and poles for solutions of the polubarinova-galin equation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-3125-3030
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2013 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 1, 259-286 p.Article in journal (Refereed) Published
Abstract [en]

We study the dynamics of roots of f'(zeta, t), where F(zeta, t) is a locally univalent polynomial solution of the Polubarinova-Galin equation for the evolution of the conformal map onto a Hele-Shaw blob subject to injection at one point. We give examples of the sometimes complicated motion of roots, but show also that the asymptotic behavior is simple. More generally we allow f'(zeta, t) to be a rational function and give sharp estimates for the motion of poles and for the decay of the Taylor coefficients. We also prove that any global in time locally univalent solution actually has to be univalent.

Place, publisher, year, edition, pages
2013. Vol. 38, no 1, 259-286 p.
Keyword [en]
Hele-Shaw flow, Laplacian growth, Polubarinova-Galin equation, Lowner-Kufarev equation, root dynamics, pole dynamics
National Category
URN: urn:nbn:se:kth:diva-121142DOI: 10.5186/aasfm.2013.3802ISI: 000316239200014ScopusID: 2-s2.0-84877662477OAI: diva2:616862

QC 20130419

Available from: 2013-04-19 Created: 2013-04-19 Last updated: 2013-04-19Bibliographically approved

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