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

Kiyoshi Mochizuki; Hideo Nakazawa; Igor Trooshin

doi:10.4171/prims/62-1-1

JournalsprimsVol. 62, No. 1pp. 1–25

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

Kiyoshi Mochizuki
Chuo University, Tokyo, Japan
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Hideo Nakazawa
Nippon Medical School, Tokyo, Japan
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- zbMATH Open
Igor Trooshin
Shinshu University, Nagano, Japan
- MathSciNet

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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