JournalsprimsVol. 62, No. 1pp. 1–25

The Principle of Limiting Amplitude for Wave Equations on a Star Graph

  • Kiyoshi Mochizuki

    Chuo University, Tokyo, Japan

  • Hideo Nakazawa

    Nippon Medical School, Tokyo, Japan

  • Igor Trooshin

    Shinshu University, Nagano, Japan
The Principle of Limiting Amplitude for Wave Equations on a Star Graph cover
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Abstract

We consider the dissipative wave propagation problem on an infinite star graph. High and low-frequency estimates and local Hölder conditions of the resolvent are studied for the reduced wave operator. Based on these results the principle of limiting amplitude is proved to hold for our wave propagation problem with oscillating external force.

Cite this article

Kiyoshi Mochizuki, Hideo Nakazawa, Igor Trooshin, The Principle of Limiting Amplitude for Wave Equations on a Star Graph. Publ. Res. Inst. Math. Sci. 62 (2026), no. 1, pp. 1–25

DOI 10.4171/PRIMS/62-1-1