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Decay and asymptotics for the 1D Klein-Gordon equation with variable coefficient cubic nonlinearities Luhrmann, Jonas
Description
The asymptotic stability analysis of one-dimensional topological solitons such as the well-known â kinkâ in the \$phi^4$ model requires an understanding of the asymptotic behavior of small solutions to 1D Klein-Gordon equations with variable coefficient quadratic and cubic nonlinearities. In this talk I will first describe the difficulties caused by variable coefficients to deal with the long-range nature of such nonlinearities. Then I will present a new result on sharp decay estimates and asymptotics for small solutions to 1D Klein-Gordon equations with constant and variable coefficient cubic nonlinearities. The main novelty of our approach is the use of pointwise-in-time local decay estimates to deal with the variable coefficient nonlinearity. If time permits, I will also discuss work in progress on the variable coefficient quadratic case, which exhibits a striking resonant interaction between the spatial oscillations of the variable coefficient and the temporal oscillations of the solutions. This is joint work with Hans Lindblad and Avy Soffer.
Item Metadata
Title |
Decay and asymptotics for the 1D Klein-Gordon equation with variable coefficient cubic nonlinearities
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-02-03T10:30
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Description |
The asymptotic stability analysis of one-dimensional topological solitons such as the well-known â kinkâ in the \$phi^4$ model requires an understanding of the asymptotic behavior of small solutions to 1D Klein-Gordon equations with variable coefficient quadratic and cubic nonlinearities.
In this talk I will first describe the difficulties caused by variable coefficients to deal with the long-range nature of such nonlinearities. Then I will present a new result on sharp decay estimates and asymptotics for small solutions to 1D Klein-Gordon equations with constant and variable coefficient cubic nonlinearities. The main novelty of our approach is the use of pointwise-in-time local decay estimates to deal with the variable coefficient nonlinearity. If time permits, I will also discuss work in progress on the variable coefficient quadratic case, which exhibits a striking resonant interaction between the spatial oscillations of the variable coefficient and the temporal oscillations of the solutions.
This is joint work with Hans Lindblad and Avy Soffer.
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Extent |
43.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Texas A&M University
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Series | |
Date Available |
2020-09-14
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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 |
10.14288/1.0394358
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Researcher
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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