Solutions of the Loewner equation with combined driving functions
Dmitri Prokhorov, Andrey Zakharov, Andrey Zherdev
TL;DR
This paper derives explicit solutions for the chordal Loewner equation with piecewise constant and combined driving functions, providing analytical and geometric descriptions of the generated traces.
Contribution
It introduces exact solutions for Loewner equations with specific piecewise driving functions, advancing understanding of their analytical and geometric properties.
Findings
Explicit solutions for piecewise constant driving functions.
Analytical description of generated traces.
Geometric interpretation of solutions.
Abstract
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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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Stability and Controllability of Differential Equations · Advanced Differential Equations and Dynamical Systems