• Complex
  • Title
  • Keyword
  • Abstract
  • Scholars
  • Journal
  • ISSN
  • Conference
搜索

Author:

Ning, Zhen-Hu (Ning, Zhen-Hu.)

Indexed by:

SCIE

Abstract:

We consider the following nonlinear Schrodinger equation on exterior domain. 1) {iu(t) + Delta(g)u + ia(x) - vertical bar u vertical bar(p-1)u=0 (x, t) is an element of Omega x (0, +infinity) u vertical bar(Gamma) = 0 l is an element of (0, +infinity) u(x, 0) = u(0)(x) x is an element of Omega, where 1 < p < n+2/n-2, Omega R-n(n >= 3) is an exterior domain and (R-n, g) is a complete Riemannian manifold. We establish Morawetz estimates for the system (1) without dissipation (a(x) 0 in (1)) and meanwhile prove exponential stability of the system (1) with a dissipation effective on a neighborhood of the infinity. It is worth mentioning that our results are different from the existing studies. First, Morawetz estimates for the system (1) are directly derived from the metric g and are independent on the assumption of an (asymptotically) Euclidean metric. In addition, we not only prove exponential stability of the system (1) with non-uniform energy decay rate, which is dependent on the initial data, but also prove exponential stability of the system (1) with uniform energy decay rate. The main methods are the development of Morawetz multipliers in non (asymptotically) Euclidean spaces and compactness-uniqueness arguments.

Keyword:

Author Community:

  • [ 1 ] [Ning, Zhen-Hu]Beijing Univ Technol, Fac Informat Technol, Beijing 100124, Peoples R China

Reprint Author's Address:

  • [Ning, Zhen-Hu]Beijing Univ Technol, Fac Informat Technol, Beijing 100124, Peoples R China

Show more details

Related Keywords:

Related Article:

Source :

MATHEMATICAL RESEARCH LETTERS

ISSN: 1073-2780

Year: 2020

Issue: 6

Volume: 27

Page: 1825-1866

1 . 0 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:46

Cited Count:

WoS CC Cited Count: 7

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 2

Affiliated Colleges:

Online/Total:780/5321944
Address:BJUT Library(100 Pingleyuan,Chaoyang District,Beijing 100124, China Post Code:100124) Contact Us:010-67392185
Copyright:BJUT Library Technical Support:Beijing Aegean Software Co., Ltd.