This guide research options of the Polubarinova-Galin and Loewner-Kufarev equations, which describe the evolution of a viscous fluid (Hele-Shaw) blob, after the time when these options have misplaced their bodily which means as a result of lack of univalence of the mapping operate concerned. When the mapping operate is not regionally univalent fascinating section transitions happen, resulting in structural adjustments within the knowledge of the answer, for instance new zeros and poles within the case of rational maps.
This matter intersects with a number of areas, together with mathematical physics, potential principle and sophisticated evaluation. The textual content might be useful to researchers and doctoral college students occupied with fluid dynamics, integrable programs, and conformal area principle.
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