A transmission problem for wave equations in infinite waveguides

被引：0

作者：

Racke, Reinhard ^{[1
]}

Yoshikawa, Shuji ^{[2
]}

机构：

[1] Univ Konstanz, Dept Math & Stat, D-78457 Constance, Germany

[2] Oita Univ, Fac Sci & Technol, Div Math Sci, 700 Dannoharu, Oita 8701192, Japan

来源：

APPLIED MATHEMATICS LETTERS | 2025年 / 163卷

关键词：

Waveguide; Transmission problem; Decay estimate; Wave equation; Composite materials;

D O I：

10.1016/j.aml.2024.109405

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a decay estimate for solutions to a transmission problem for wave equations with different propagation speeds in an infinite waveguide. The problem represents the wave propagation in unbounded and layered composite materials in which different properties are given. It is a new composition of a waveguide problem and a transmission problem, motivated by a unit cell model for CFRP. The proof is based on splitting variables, partial eigenfunction expansions in the bounded cross section, and on an explicit Weyl type estimate for the eigenvalues.

引用

页数：5

共 50 条

[1] Nonlinear hyperbolic equations in infinite homogeneous waveguides
Metcalfe, J
Sogge, CD
Stewart, A
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2005, 30 (4-6) : 643 - 661
[2] Memory-type boundary stabilization of a transmission problem for Kirchhoff wave equations
Fan, Sheng
Feng, Baowei
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (13) : 8179 - 8192
[3] Stability of a transmission problem for Kirchhoff-type wave equations with memory on the boundary
Park, Sun-Hye
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (10) : 3528 - 3537
[4] WELL-POSEDNESS AND ENERGY DECAY OF A TRANSMISSION PROBLEM OF KIRCHHOFF TYPE WAVE EQUATIONS WITH DAMPING AND DELAY TERMS
Liu, Zhiqing
Gao, Cunchen
Fang, Zhong Bo
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, : 1 - 23
[5] Stability for an Interface Transmission Problem of Wave-Plate Equations with Dynamical Boundary Controls
Abdallah, Zahraa
Gerbi, Stephane
Kassem, Chiraz
Wehbe, Ali
ACTA APPLICANDAE MATHEMATICAE, 2023, 188 (01)
[6] GENERAL DECAY OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY MEMORY CONDITION
Sun Hye PARK
Acta Mathematica Scientia, 2014, 34 (05) : 1395 - 1403
[7] Stability for an Interface Transmission Problem of Wave-Plate Equations with Dynamical Boundary Controls
Zahraa Abdallah
Stéphane Gerbi
Chiraz Kassem
Ali Wehbe
Acta Applicandae Mathematicae, 2023, 188
[8] GENERAL DECAY OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY MEMORY CONDITION
Park, Sun Hye
ACTA MATHEMATICA SCIENTIA, 2014, 34 (05) : 1395 - 1403
[9] Exponential Stability for a Transmission Problem of a Viscoelastic Wave Equation
Marcelo M. Cavalcanti
Emanuela R. S. Coelho
Valéria N. Domingos Cavalcanti
Applied Mathematics & Optimization, 2020, 81 : 621 - 650
[10] Exponential Stability for a Transmission Problem of a Viscoelastic Wave Equation
Cavalcanti, Marcelo M.
Coelho, Emanuela R. S.
Cavalcanti, Valeria N. Domingos
APPLIED MATHEMATICS AND OPTIMIZATION, 2020, 81 (02) : 621 - 650

← 1 2 3 4 5 →