Math. Model. Nat. Phenom.
Volume 15, 2020
|Number of page(s)||14|
|Published online||17 February 2020|
Integrability-preserving regularizations of Laplacian Growth
4202 E. Fowler Ave., CMC342,
FL 33620, USA.
* Corresponding author: email@example.com
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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