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Variational principles and conservation laws in the derivation of radiation boundary conditions for wave equations


Authors: Edwin F. G. van Daalen, Jan Broeze and Embrecht van Groesen
Journal: Math. Comp. 58 (1992), 55-71
MSC: Primary 35L05; Secondary 35A15, 35L65, 35Q53, 65N99
DOI: https://doi.org/10.1090/S0025-5718-1992-1106985-6
MathSciNet review: 1106985
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Abstract: Radiation boundary conditions are derived for partial differential equations which describe wave phenomena. Assuming the evolution of the system to be governed by a Lagrangian variational principle, boundary conditions are obtained with Noether's theorem from the requirement that they transmit some appropriate density--such as the energy density--as well as possible.

The theory is applied to a nonlinear version of the Klein-Gordon equation. For this application numerical test results are presented. In an accompanying paper the theory is applied to a two-dimensional wave equation.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1992-1106985-6
Keywords: Radiation boundary conditions, variational principles, conservation laws, wave equations
Article copyright: © Copyright 1992 American Mathematical Society