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Published March 1986 | Published
Journal Article Open

Exact Boundary Conditions at an Artificial Boundary for Partial Differential Equations in Cylinders


The numerical solution of partial differential equations in unbounded domains requires a finite computational domain. Often one obtains a finite domain by introducing an artificial boundary and imposing boundary conditions there. This paper derives exact boundary conditions at an artificial boundary for partial differential equations in cylinders. An abstract theory is developed to analyze the general linear problem. Solvability requirements and estimates of the solution of the resulting finite problem are obtained by use of the notions of exponential and ordinary dichotomies. Useful representations of the boundary conditions are derived using separation of variables for problems with constant tails. The constant tail results are extended to problems whose coefficients obtain limits at infinity by use of an abstract perturbation theory. The perturbation theory approach is also applied to a class of nonlinear problems. General asymptotic formulas for the boundary conditions are derived and displayed in detail.

Additional Information

© 1986 Society for Industrial and Applied Mathematics. Received by the editors April 5, 1984. This research was sponsored by the U.S. Army under contract DAAG29-80-C-0041, and supported in part by the U.S. Department of Energy under contract DE-AS03-76SF-00767.

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