The boundness of the operator-valued functions for multidimensional nonlinear wave equations with applications

DOI10.1016/j.aml.2017.04.026zbMath1379.35189OpenAlexW2618502920MaRDI QIDQ2411129

Chang Ying Liu, Xin-Yuan Wu

Publication date: 20 October 2017

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2017.04.026

zbMATH Keywords

energy-preserving schemeoperator-variation-of-constants formuladifferent boundary conditionsenergy-preserving formulaHamiltonian wave equation

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Theoretical approximation in context of PDEs (35A35)

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Cites Work

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• An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations
• Semigroups of linear operators and applications to partial differential equations
• Efficient energy-preserving integrators for oscillatory Hamiltonian systems
• An analytical expression of solutions to nonlinear wave equations in higher dimensions with Robin boundary conditions
• An integral formula adapted to different boundary conditions for arbitrarily high-dimensional nonlinear Klein-Gordon equations with its applications
• Spectral Methods
• Geometric integration using discrete gradients
• One-Parameter Semigroups for Linear Evolution Equations
• A new framework for solving partial differential equations using semi-analytical explicit RK(N)-type integrators

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