Webster's equation with curvature and dissipation

Details Webster's equation with curvature and dissipation Webster's equation with curvature and dissipation

2012-04-18

arxiv.org/abs/1204.4075v1

Mathematics

Analysis of PDEs

20pp., 4pp. appendix, 1 figure

Scientific paper

Wave propagation in curved tubular domains is considered. Starting from the wave equation with dissipative boundary conditions, a general version of Webster's equation is derived: it is shown that certain averages of any solution of the wave equation satisfy the corresponding Webster's equation which modified with additional control signals extracted from the wave equation. This result is used in the companion paper to give an a posteriori estimate for the error between these averages and the solution of the unmodified Webster's equation.

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