منابع مشابه
Hyperbolic singular perturbations for integrodifferential equations
We study the convergence of solutions of * Co E-m (T.-J. X 0096-3 doi:10. e2u00ðt; eÞ þ u0ðt; eÞ 1⁄4 ðeAþ BÞuðt; eÞ þ R t 0 Kðt sÞðeAþ BÞuðs; eÞds þf ðt; eÞ; tP 0; uð0; eÞ 1⁄4 u0ðeÞ; u0ð0; eÞ 1⁄4 u1ðeÞ; 8< : to solutions of w0ðtÞ 1⁄4 BwðtÞ þ R t 0 Kðt sÞBwðsÞdsþ f ðtÞ; tP 0; wð0Þ 1⁄4 w0; when e ! 0. Here A and B are linear unbounded operators in a Banach space X , KðtÞ is a linear bounded opera...
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By virtue of an operator-theoretical approach, we deal with hyperbolic singular perturbation problems for integrodifferential equations. New convergence theorems for such singular perturbation problems are obtained, which generalize some previous results by This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, an...
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and Applied Analysis 3 Define a function m t by m t v t ∫ t 0 g s v s ds v t ∫ t 0 g s ds, 2.5 then m 0 v 0 u0, v t ≤ m t , v′ t ≤ f t m t , 2.6 m′ t 2g t v t v′ t ( 1 ∫ t 0 g s ds ) ≤ m t [ 2g t f t ( 1 ∫ t 0 g s ds )] . 2.7 Integrating 2.7 from 0 to t, we have m t ≤ u0 exp (∫ t 0 ( 2g s f s ( 1 ∫ s 0 g σ dσ )) ds ) . 2.8 Using 2.8 in 2.6 , we obtain v′ t ≤ u0f t exp (∫ t 0 ( 2g s f s ( 1 ∫ s ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0352718-2