| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Growth phenomena
|
|
|---|---|---|
| Article Number | 9 | |
| Number of page(s) | 14 | |
| DOI | https://doi.org/10.1051/mmnp/2019032 | |
| Published online | 17 February 2020 | |
Integrability-preserving regularizations of Laplacian Growth
4202 E. Fowler Ave., CMC342,
Tampa,
FL 33620, USA.
* Corresponding author: razvan@usf.edu
Received:
17
December
2018
Accepted:
16
July
2019
The Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary singularity formation. A discrete counterpart, Diffusion-Limited Aggregation (or DLA), has a similar local growth law, but significantly different global behavior. For both LG and DLA, a proper description for the scaling properties of long-time solutions is not available yet. In this note, we outline a possible approach towards finding the correct theory yielding a regularized LG and its relation to DLA.
Mathematics Subject Classification: 30D05 / 30E10 / 30E25
Key words: Integrable systems / free boundary problem / quadratic differentials
© EDP Sciences, 2020
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