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March 2003 Self-Similar Solutions for Nonlinear Schrodinger Equations
Changxing Miao, Bo Zhang, Xiaoyi Zhang
Methods Appl. Anal. 10(1): 119-136 (March 2003).

Abstract

In this paper we study self-similar solutions for nonlinear Schrodinger equations using a scaling technique and the partly contractive mapping method. We establish the small global well-posedness of the Cauchy problem for nonlinear Schrodinger equations in some non-reflexive Banach spaces which contain many homogeneous functions. This we do by establishing some a priori nonlinear estimates in Besov spaces, employing the mean difference characterization and multiplication in Besov spaces. These new global solutions to nonlinear Schrodinger equations with small data admit a class of self-similar solutions. Our results improve and extend the well-known results of Planchon [18], Cazenave and Weissler [4, 5] and Ribaud and Youssfi [20].

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Changxing Miao. Bo Zhang. Xiaoyi Zhang. "Self-Similar Solutions for Nonlinear Schrodinger Equations." Methods Appl. Anal. 10 (1) 119 - 136, March 2003.

Information

Published: March 2003
First available in Project Euclid: 16 June 2005

zbMATH: 1076.35118
MathSciNet: MR2014165

Rights: Copyright © 2003 International Press of Boston

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Vol.10 • No. 1 • March 2003
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