# The Boundary Integral Equation for Kinetically Limited Dendrite Growth

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## Abstract

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## 1. Introduction

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## 2. Two-Dimensional BIE for Solidifying Pure Liquid

## 3. Two-Dimensional BIE for Solidifying Pure and/or Binary Liquid

## 4. Three-Dimensional BIE for a Paraboloid of Revolution and Elliptic Paraboloid Growing from Undercooled Binary Liquid

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

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**Figure 2.**(

**a**) The interface function $\zeta $ versus $\Delta /\beta V$ at fixed $x=1$ and t. (

**b**) The interface function $\zeta $ versus spatial coordinate x at fixed $\Delta /\beta V=1$ and t. The calculations are made according to Equation (6).

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**MDPI and ACS Style**

Titova, E.A.; Galenko, P.K.; Nikishina, M.A.; Toropova, L.V.; Alexandrov, D.V.
The Boundary Integral Equation for Kinetically Limited Dendrite Growth. *Axioms* **2023**, *12*, 1016.
https://doi.org/10.3390/axioms12111016

**AMA Style**

Titova EA, Galenko PK, Nikishina MA, Toropova LV, Alexandrov DV.
The Boundary Integral Equation for Kinetically Limited Dendrite Growth. *Axioms*. 2023; 12(11):1016.
https://doi.org/10.3390/axioms12111016

**Chicago/Turabian Style**

Titova, Ekaterina A., Peter K. Galenko, Margarita A. Nikishina, Liubov V. Toropova, and Dmitri V. Alexandrov.
2023. "The Boundary Integral Equation for Kinetically Limited Dendrite Growth" *Axioms* 12, no. 11: 1016.
https://doi.org/10.3390/axioms12111016