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New multiple end solutions in the Allen-Cahn and the generalized second Painlevà ¨ equation. Kowalczyk, Michal
Description
In this talk I will discuss two new constructions of the multiple end solutions. In the case of the Allen-Cahn equation the ends are asymptotic to the Simons cone in $\mathbb R^8$. The case of the generalized second Painlev\'e equation in $\mathbb R^2$ is somehow different since there is no apparent underlying geometric problem. Yet we can interpret the behavior of the solution as being asymptotic along the axis to: two one dimensional Hastings-McLeod solution, the heteroclinic solution of the Allen-Cahn equation and the trivial solution.
Item Metadata
| Title |
New multiple end solutions in the Allen-Cahn and the generalized second Painlevà ¨ equation.
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2019-05-07T14:02
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| Description |
In this talk I will discuss two new constructions of the multiple end solutions. In the case of the Allen-Cahn equation the ends are asymptotic to the Simons cone in $\mathbb R^8$. The case of the generalized second Painlev\'e equation in $\mathbb R^2$ is somehow different since there is no apparent underlying geometric problem. Yet we can interpret the behavior of the solution as being asymptotic along the axis to: two one dimensional Hastings-McLeod solution, the heteroclinic solution of the Allen-Cahn equation and the trivial solution.
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| Extent |
30.0 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Universidad de Chile
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| Series | |
| Date Available |
2019-11-04
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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 |
10.14288/1.0384910
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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