A non-steady flow of liquid in a porous pipe with variable permeability |
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Authors: | Avner Friedman Robert Jensen |
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Institution: | 1. Department of Mathematics, Northwestern University, Evanston, Illinois 60201 USA;2. Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506 USA |
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Abstract: | LetB denote the infinitesimal operator of a strongly continuous semigroup S(t), with resolvent Rλ, on Banach space L. We define related operators P and V so that λRλf = Pf + λVf + o(λ), as λ → 0+. For α, η > 0 and possibly unbounded, linear operator A, we let Uα, η(t) represent a strongly continuous semigroup generated by αA + ηB. We show that under appropriate simultaneous convergence of α and η, Uα, η(t) converges strongly to a strongly continous semigroup U(t), having infinitesimal operator characterized through PA(VA)rf where r =min{j ? 0, PA(VA)j ≠ 0}. We apply the abstract perturbation theorem to a singular perturbation initial-value problem, of Tihonov-type, for a non-linear system of ordinary differential equations. |
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