Global dynamics below a threshold for the nonlinear Schrödinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph

Masaru Hamano (), Masahiro Ikeda (), Takahisa Inui () and Ikkei Shimizu ()
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Masaru Hamano: Waseda University
Masahiro Ikeda: Keio University
Takahisa Inui: Osaka University
Ikkei Shimizu: Osaka University

Partial Differential Equations and Applications, 2024, vol. 5, issue 1, 1-36

Abstract: Abstract We consider the nonlinear Schrödinger equations on the star graph with the Kirchhoff boundary and the repulsive Dirac delta boundary at the origin. In the present paper, we show the scattering-blowup dichotomy result below the mass-energy of the ground state on the real line. The proof of the scattering part is based on a concentration compactness and rigidity argument. Our main contribution is to give a linear profile decomposition on the star graph by using a symmetric decomposition.

Keywords: Nonlinear Schrödinger equation; Star graph; Scattering; Blow-up; Profile decomposition; 35B40; 35Q55; 35R02 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42985-024-00274-2

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