Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. II: Taking into account a source on the right-hand side and a weak dispersion

DOI10.1134/S1061920808040018zbMath1194.35054OpenAlexW1969735088MaRDI QIDQ1033799

Brunello Tirozzi, S. Yu. Dobrokhotov, Daniela Bianchi

Publication date: 10 November 2009

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920808040018

zbMATH Keywords

weak dispersion

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (5)

Homogenization of the Cauchy Problem for the Wave Equation with Rapidly Varying Coefficients and Initial Conditions ⋮ Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients ⋮ Approximation of solutions of the two-dimensional wave equation with variable velocity and localized right-hand side using some ``simple solutions ⋮ Asymptotic solutions of 2D wave equations with variable velocity and localized right-hand side ⋮ On mechanical waves and Doppler shifts from moving boundaries

Cites Work

• Asymptotic expansions and the Maslov canonical opeator in the linear theory of water waves. I: Main constructions and equations for surface gravity waves
• Asymptotics of localized solutions of the one-dimensional wave equation with variable velocity. I: The Cauchy problem
• Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations
• Asymptotic fast-decreasing solutions of linear, strictly hyperbolic systems with variable coefficients
• Description of tsunami propagation based on the Maslov canonical operator
• Focused tsunami waves
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