標題: | Convergence of the Klein-Gordon equation to the wave map equation with magnetic field |
作者: | Wu, Kung-Chien 數學建模與科學計算所(含中心) Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics |
關鍵字: | Klein-Gordon equation;Magnetic field;Wave map equation;Nonrelativistic-semiclassical limit |
公開日期: | 15-三月-2010 |
摘要: | This paper is devoted to the proof of the convergence from the modulated cubic nonlinear defocusing Klein-Gordon equation with magnetic field to the wave map equation. More precisely, we discuss the nonrelativistic-semiclassical limit of the modulated cubic nonlinear Klein-Gordon equation with magnetic field where the Planck's constant h = epsilon and the speed of light c are related by c = epsilon(-alpha) for some alpha >= 1. When alpha = 1 the limit wave function satisfies the wave map with one extra term coming from the magnetic field. However, alpha > 1, the effect of the magnetic filed disappears and the limit is the typical wave map equation only. (C) 2009 Elsevier Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.jmaa.2009.11.022 http://hdl.handle.net/11536/5725 |
ISSN: | 0022-247X |
DOI: | 10.1016/j.jmaa.2009.11.022 |
期刊: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
Volume: | 365 |
Issue: | 2 |
起始頁: | 584 |
結束頁: | 589 |
顯示於類別: | 期刊論文 |