Abstract
We consider semilinear parabolic equations ut= uxx+ f(u) on R. We give an overview of results on the large time behavior of bounded solutions, focusing in particular on their limit profiles as t→ ∞ with respect to the locally uniform convergence. The collection of such limit profiles, or, the ω -limit set of the solution, always contains a steady state. Questions of interest then are whether—or under what conditions—the ω -limit set consists of steady states, or even a single steady state. We give several theorems and examples pertinent to these questions.
Original language | English (US) |
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Title of host publication | Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday |
Editors | Pavel Gurevich, Juliette Hell, Arnd Scheel, Bjorn Sandstede |
Publisher | Springer New York LLC |
Pages | 172-183 |
Number of pages | 12 |
ISBN (Print) | 9783319641720 |
DOIs | |
State | Published - 2017 |
Event | Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016 - Berlin, Germany Duration: Jul 25 2016 → Jul 29 2016 |
Publication series
Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 205 |
ISSN (Print) | 2194-1009 |
ISSN (Electronic) | 2194-1017 |
Other
Other | Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016 |
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Country/Territory | Germany |
City | Berlin |
Period | 7/25/16 → 7/29/16 |
Bibliographical note
Funding Information:Dedicated to Bernold Fiedler on the occasion of his 60th birthday. Supported in part by the NSF Grant DMS-1565388.
Keywords
- Asymptotic behavior
- Convergence
- Entire solutions
- Quasiconvergence
- Semilinear heat equation on the real line