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Dynamics around the ground state of a nonlinear evolution equation

✍ Scribed by Jorge A. Esquivel-Avila

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
163 KB
Volume
63
Category
Article
ISSN
0362-546X

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✦ Synopsis

We analyze the qualitative behavior of solutions forwards and backwards. We present characterizations of blowup, boundedness and convergence to the ground state as t → ±∞. We define and use a potential well and several invariant and positive invariant sets.

📜 SIMILAR VOLUMES

Controllability of the nonlinear Schrödi
Controllability of the nonlinear Schrödinger equation in the vicinity of the ground state
✍ H. Lange; H. Teismann 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 213 KB

## Abstract Local exact controllability of the one‐dimensional NLS (subject to zero‐boundary conditions) with distributed control is shown to hold in a __H__^1^‐neighbourhood of the nonlinear ground state. The __Hilbert Uniqueness Method__ (__HUM__), due to Lions, is applied to the linear control p