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2022 The compact interface property for the stochastic heat equation with seed bank
Florian Nie
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Electron. Commun. Probab. 27: 1-15 (2022). DOI: 10.1214/22-ECP465

Abstract

We investigate the compact interface property in a recently introduced variant of the stochastic heat equation that incorporates dormancy, or equivalently seed banks. There individuals can enter a dormant state during which they are no longer subject to spatial dispersal and genetic drift. This models a state of low metabolic activity as found in microbial species. Mathematically, one obtains a memory effect since mass accumulated by the active population will be retained for all times in the seed bank. This raises the question whether the introduction of a seed bank into the system leads to a qualitatively different behaviour of a possible interface. Here, we aim to show that nevertheless in the stochastic heat equation with seed bank compact interfaces are retained through all times in both the active and dormant population. We use duality and a comparison argument with partial functional differential equations to tackle technical difficulties that emerge due to the lack of the martingale property of our solutions which was crucial in the classical non seed bank case.

Funding Statement

The author gratefully acknowledges financial support from the Berlin Mathematical School (BMS) and the IRTG 2544 “Stochastic Analysis in Interaction”.

Acknowledgments

The author wishes to thank Andras Tobias and Jochen Blath for useful discussion and comments.

Citation

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Florian Nie. "The compact interface property for the stochastic heat equation with seed bank." Electron. Commun. Probab. 27 1 - 15, 2022. https://doi.org/10.1214/22-ECP465

Information

Received: 9 August 2021; Accepted: 16 April 2022; Published: 2022
First available in Project Euclid: 4 May 2022

Digital Object Identifier: 10.1214/22-ECP465

Subjects:
Primary: 35R10 , 60H15

Keywords: Compact interface , dormancy , Duality , seed bank , Stochastic heat equation

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