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Abstract We analyze spatial spreading in a population model with logistic growth and chemorepulsion. In a parameter range of short-range chemo-diffusion, we use geometric singular perturbation theory and functional-analytic farfield-core decompositions to identify spreading speeds with marginally stable front profiles. In particular, we identify a sharp boundary between between linearly determined, pulled propagation, and nonlinearly determined, pushed propagation, induced by the chemorepulsion. The results are motivated by recent work on singular limits in this regime using PDE methods (Grietteet al2023J. Funct. Anal.285110115).
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This content will become publicly available on June 1, 2026
A flow‐type scaling limit for random growth with memory
Abstract We study a stochastic Laplacian growth model, where a set grows according to a reflecting Brownian motion in stopped at level sets of its boundary local time. We derive a scaling limit for the leading‐order behavior of the growing boundary (i.e., “interface”). It is given by a geometric flow‐typepde. It is obtained by an averaging principle for the reflecting Brownian motion. We also show that this geometric flow‐typepdeis locally well‐posed, and its blow‐up times correspond to changes in the diffeomorphism class of the growth model. Our results extend those of Dembo et al., which restricts to star‐shaped growth domains and radially outwards growth, so that in polar coordinates, the geometric flow transforms into a simpleodewith infinite lifetime. Also, we remove the “separation of scales” assumption that was taken in Dembo et al.; this forces us to understand the local geometry of the growing interface.
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- Award ID(s):
- 1954337
- PAR ID:
- 10627680
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Communications on Pure and Applied Mathematics
- Volume:
- 78
- Issue:
- 6
- ISSN:
- 0010-3640
- Page Range / eLocation ID:
- 1147 to 1198
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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