Long-term analysis of semilinear wave equations with slowly varying wave speed

DOI10.1080/03605302.2016.1235581zbMath1368.35164arXiv1602.06748OpenAlexW2283867267MaRDI QIDQ2955382

Christian Lubich, Ludwig J. Gauckler, Ernst Hairer

Publication date: 25 January 2017

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.06748

zbMATH Keywords

Dirichlet boundary conditionsadiabatic invariantsmall initial datamodulated Fourier expansionlong-time existence

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11) Second-order semilinear hyperbolic equations (35L71)

Related Items (5)

Response solutions for wave equations with variable wave speed and periodic forcing ⋮ Numerical conservations of energy, momentum and actions in the full discretisation for nonlinear wave equations ⋮ A two-step symmetric method for charged-particle dynamics in a normal or strong magnetic field ⋮ A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian systems ⋮ Long-time momentum and actions behaviour of energy-preserving methods for semi-linear wave equations via spatial spectral semi-discretisations

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