Math. Model. Nat. Phenom.
Volume 15, 2020
|Number of page(s)||24|
|Published online||14 February 2020|
On integrability and exact solvability in deterministic and stochastic Laplacian growth
Laboratoire de Physique Mathematique, Centre de recherches mathématiques, Université de Montréal,
P.O. Box 6128,
Centre-ville Station Montréal (Québec)
H3C 3J7, Canada.
* Corresponding author: email@example.com
Accepted: 18 July 2019
We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical mechanics. We also review important exact results obtained in the theory of multi-fractal spectra of the stochastic models related to the Laplacian growth: Schramm-Loewner and Levy-Loewner evolutions.
Mathematics Subject Classification: 31B20 / 35R35 / 82B24 / 76M40 / 76D27 / 37K10 / 15B52 / 60J67
Key words: Laplacian growth / elliptic growth / integrable and exactly-solvable models / multi-fractal systems
© EDP Sciences, 2020
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