Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation
| Autor: | Alex H. Ardila, Mykael Cardoso |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Computer Science::Information Retrieval Applied Mathematics 010102 general mathematics General Medicine 01 natural sciences Instability 010101 applied mathematics Nonlinear system symbols.namesake Flow (mathematics) Bounded function symbols 0101 mathematics Finite time Invariant (mathematics) Nonlinear Schrödinger equation Analysis Mathematical physics |
| Zdroj: | Communications on Pure & Applied Analysis. 20:101-119 |
| ISSN: | 1553-5258 |
| DOI: | 10.3934/cpaa.2020259 |
| Popis: | Using variational methods we study the stability and strong instability of ground states for the focusing inhomogeneous nonlinear Schrodinger equation (INLS) \begin{document}$ \begin{equation*} i\partial_{t}u+\Delta u+|x|^{-b}|u|^{p-1}u = 0. \end{equation*} $\end{document} We construct two kinds of invariant sets under the evolution flow of (INLS). Then we show that the solution of (INLS) is global and bounded in \begin{document}$ H^{1}(\mathbb{R^{N}}) $\end{document} in the first kind of the invariant sets, while the solution blow-up in finite time in the other invariant set. Consequently, we prove that if the nonlinearity is \begin{document}$ L^{2} $\end{document} -supercritical, then the ground states are strongly unstable by blow-up. |
| Databáze: | OpenAIRE |
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