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Title: Linear Approximation and Asymptotic Expansion of Solutions in Many Small Parameters for a Nonlinear Kirchhoff Wave Equation with Mixed Nonhomogeneous Conditions
Authors: Le, Thi Phuong Ngoc
Nguyen, Thanh Long
Keywords: Faedo–Galerkin method;Linear recurrent sequence;Asymptotic expansion of order N +1
Issue Date: 2010
Abstract: In this paper, we consider the following nonlinear Kirchhoff wave equation ⎧⎪⎨ ⎪⎩ utt − ∂ ∂x (μ(u, ux 2)ux ) = f (x, t,u,ux,ut ), 0<x <1, 0 < t <T, ux (0, t) = g(t), u(1, t) = 0, u(x, 0) = u 0(x), ut (x, 0) = u 1(x), (1) where u 0, u 1, μ, f , g are given functions and ux 2 = 1 0 u2 x(x, t)dx. To the problem (1), we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved by applying the Faedo–Galerkin method and the weak compact method. In particular, motivated by the asymptotic expansion of a weak solution in only one, two or three small parameters in the researches before now, an asymptotic expansion of a weak solution in many small parameters appeared on both sides of (1)1 is studied.
Description: TNS06114 ; ACTA APPLICANDAE MATHEMATICAE Volume: 112 Issue: 2 Pages: 137-169
ISSN: 0167-8019
Appears in Collections:Bài báo của ĐHQGHN trong Web of Science

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