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Interfaces in the Fisher equation and a Hamilton-Jacobi equation Yanagida, Eiji
Description
We consider the dynamics of interfaces in the Fisher-KPP equation. It is known that solutions of this equation exhibit interfaces that correspond to transition layers from the trivial steady state to a positive steady state. If an initial value decays rapidly in space, then the interface moves with a constant speed that is equal to the minimal speed of traveling fronts in one-dimensional space. On the other hand, it is known that if an initial value decays slowly, the interface may move in a rather irregular way. In this talk, we show that the dynamics of interfaces for slowly decaying initial data can be described as a level set of a Hamilton-Jacobi equation. We also discuss properties of solutions of the Hamilton-Jacobi equation. This is a joint work with Hirokazu Ninomiya (Meiji University).
Item Metadata
Title |
Interfaces in the Fisher equation and a Hamilton-Jacobi equation
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2015-09-01T14:20
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Description |
We consider the dynamics of interfaces in the Fisher-KPP equation. It is known that solutions of this equation exhibit interfaces that correspond to transition layers from the trivial steady state to a positive steady state. If an initial value decays rapidly in space, then the interface moves with a constant speed that is equal to the minimal speed of traveling fronts in one-dimensional space. On the other hand, it is known that if an initial value decays slowly, the interface may move in a rather irregular way. In this talk, we show that the dynamics of interfaces for slowly decaying initial data can be described as a level set of a Hamilton-Jacobi equation. We also discuss properties of solutions of the Hamilton-Jacobi equation.
This is a joint work with Hirokazu Ninomiya (Meiji University).
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Extent |
47 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Tokyo Institute of Technology
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Series | |
Date Available |
2017-01-28
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0340329
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International