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

Author

Listed:
  • Masaru Hamano

    (Waseda University)

  • Masahiro Ikeda

    (Keio University
    Center for Advanced Intelligence Project, RIKEN)

  • Takahisa Inui

    (Osaka University)

  • Ikkei Shimizu

    (Osaka University)

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.

Suggested Citation

  • Masaru Hamano & Masahiro Ikeda & Takahisa Inui & Ikkei Shimizu, 2024. "Global dynamics below a threshold for the nonlinear Schrödinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph," Partial Differential Equations and Applications, Springer, vol. 5(1), pages 1-36, February.
    • Handle: RePEc:spr:pardea:v:5:y:2024:i:1:d:10.1007_s42985-024-00274-2
    DOI: 10.1007/s42985-024-00274-2
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