Nonlinear wave equation with damping: Periodic forcing and non‐resonant solutions to the Kuznetsov equation

DOI10.1002/zamm.201600280arXiv1611.08883OpenAlexW2963441052MaRDI QIDQ6064387

Aday Celik, Mads Kyed

Publication date: 12 December 2023

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.08883

zbMATH Keywords

periodic solutionswave equationdamping

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to PDEs (35B10) Resonance in context of PDEs (35B34) Second-order semilinear hyperbolic equations (35L71)

Related Items (4)

Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation ⋮ Primitive equations with horizontal viscosity: the initial value and the time-periodic problem for physical boundary conditions ⋮ If time were a graph, what would evolution equations look like? ⋮ Nonlinear acoustics: Blackstock-Crighton equations with a periodic forcing term

Cites Work

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• Effect of resonance on the existence of periodic solutions for strongly damped wave equation
• Well-posedness of the Westervelt and the Kuznetsov equation with nonhomogeneous Neumann boundary conditions
• Global well-posedness and exponential stability for Kuznetsov's equation in \(L_p\)-spaces
• On \(L_ p\) multipliers
• An analysis of nonhomogeneous Kuznetsov's equation: Local and global well-posedness; exponential decay
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I

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