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arXiv · 2212.06411

Global dynamics below a threshold for the nonlinear Schr\"odinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph

Masaru Hamano·Masahiro Ikeda·Takahisa Inui·Ikkei Shimizu
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Abstract

We consider the nonlinear Schr\"odinger 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 symmetrical decomposition.

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Masaru Hamano, Masahiro Ikeda, Takahisa Inui, Ikkei Shimizu. 2022-12-13. Global dynamics below a threshold for the nonlinear Schr\"odinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph. https://arxiv.org/abs/2212.06411

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