Blow-up rate, mass concentration and asymptotic profile of blow-up solutions for the nonlinear inhomogeneous Schrödinger equation

Zhu, Shihui; Yang, Han; Zhang, Jian

doi:10.1016/j.amc.2014.06.061

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2018

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“…Meantime, Fibich and Wang investigated the case K ( x ): = K ( ε | x |), where ε > 0 is small enough and

K \in C^{4} false(R^{N} false) ⋂ L^{\infty} false(R^{N} false)

. In addition, the case K ( x ) = | x | − b is studied by many authors, one can refer to other studies() and references therein. Especially, when b = 0, it becomes the classical nonlinear Schrödinger equation, which has been studied extensively over the last three decades (see other studies() and references therein).…”

Section: Introductionmentioning

confidence: 99%

Blow‐up dynamics of L²−critical inhomogeneous nonlinear Schrödinger equation

Peng

Zhao

2018

Math Methods in App Sciences

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The purpose of this work is to study the L 2 −critical focusing inhomogeneous nonlinear Schrödinger equationWe study the dynamical behavior for blow-up solutions when initial date ∈ H 1 (R N ) and satisfies || || L 2 ≥ ||Q|| L 2 , where Q is the ground state solution of our problem. Furthermore, we obtain the determination of the blow-up solutions when || || L 2 = ||Q|| L 2 . KEYWORDS blow-up, dynamical behavior, profile decomposition 9408

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“…Meantime, Fibich and Wang investigated the case K ( x ): = K ( ε | x |), where ε > 0 is small enough and