Blow‐up dynamics of L2−critical inhomogeneous nonlinear Schrödinger equation. (4th October 2018)

• Record Type: Journal Article
• Authors: Peng, Congming; Zhao, Dun
• Other Names: Anguelov Roumen guestEditor.; Banasiak Jacek guestEditor.; Debbouche Amar guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 18(2018)
• Page Start: 9408
• Page End: 9421
• Publication Date: 2018-10-04
• Subjects: blow‐up -- dynamical behavior -- profile decomposition; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5300
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The purpose of this work is to study the L 2 −critical focusing inhomogeneous nonlinear Schrödinger equation i ∂ t u = − Δ u − | x | − b | u | 4 − 2 b N u, ( t, x ) ∈ R × R N, with 0 < b < 1. We study the dynamical behavior for blow‐up solutions when initial date ϕ ∈ H 1 ( R N ) and satisfies ‖ ϕ ‖ 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 ‖ ϕ ‖ L 2 = ‖ Q ‖ L 2 .