Abstract
In this work a justification for the following formal perturbation methods is presented:
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(i)
Luke's procedure for equations of the type φtt−φss=εf(φ).
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(ii)
The Chikwendu-Kevorkian perturbation method for equations of the type φtt−φss=εf(φt, φs).
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(iii)
The Krylov-Bogoljubov-Mitropolski-Montgomery-Tidman approach for equations of the type φtt−φss+p2φ=εf(φ, φt, φs).
The justification implies a proof of the validity of the asymptotic approximations for the initial value problem: φ=φ(t,s), t⩾0, −∞<s<∞, φ(0,s)=ρ(s), φt(0,s)=μ(s).
As a mathematical tool the theory of integral inequalities is used.
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© 1979 Springer-Verlag
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van der Burgh, A.H.P. (1979). On the asymptotic validity of perturbation methods for hyperbolic differential equations. In: Verhulst, F. (eds) Asymptotic Analysis. Lecture Notes in Mathematics, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062956
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DOI: https://doi.org/10.1007/BFb0062956
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09245-2
Online ISBN: 978-3-540-35332-4
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