Finite-time Blowup for some Nonlinear Complex Ginzburg–Landau Equations
| Autor: | Thierry Cazenave, Seifeddine Snoussi |
|---|---|
| Přispěvatelé: | Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut préparatoire aux études scientifiques et techniques [La Marsa] (IPEST) |
| Rok vydání: | 2019 |
| Předmět: |
Complex Ginzburg-Landau equation
Pure mathematics 010102 general mathematics Mathematics::Analysis of PDEs finite-time blowup variance 01 natural sciences 010101 applied mathematics Nonlinear system [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Finite time Ginzburg landau Energy (signal processing) energy Mathematics |
| Zdroj: | Partial Differential Equations Arising from Physics and Geometry Partial Differential Equations Arising from Physics and Geometry, 450, Cambridge University Press, 2019, London Mathematical Society Lecture Note Series, 9781108367639. ⟨10.1017/9781108367639.004⟩ |
| DOI: | 10.1017/9781108367639.004 |
| Popis: | International audience; In this article, we review finite-time blowup criteria for the family of complex Ginzburg-Landau equations $u_t = e^{ i\theta } [\Delta u + |u|^\alpha u] + \gamma u$ on ${\mathbb R}^N $, where $0 \le \theta \le \frac {\pi } {2}$, $\alpha >0$ and $\gamma \in {\mathbb R} $. We study in particular the effect of the parameters $\theta $ and $\gamma $, and the dependence of the blowup time on these parameters. |
| Databáze: | OpenAIRE |
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