Solutions of the Loewner equation with combined driving functions

  title={Solutions of the Loewner equation with combined driving functions},
  author={Dmitri Prokhorov and Andrey Zakharov and Andrey Zherdev},
  journal={Izvestia of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics},
The paper is devoted to the multiple chordal Loewner differential equation with different driving functions on two time intervals. We obtain exact implicit or explicit solutions to the Loewner equations with piecewise constant driving functions and with combined constant and square root driving functions. In both cases, there is an analytical and geometrical description of generated traces. 
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