Please use this identifier to cite or link to this item: http://repository.vnu.edu.vn/handle/VNU_123/28987
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
Publisher: SPRINGER, VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS
Citation: ISIKNOWLEDGE
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
URI: http://repository.vnu.edu.vn/handle/VNU_123/28987
https://link.springer.com/article/10.1007/s10440-009-9555-9
ISSN: 0167-8019
Appears in Collections:Bài báo của ĐHQGHN trong Web of Science

Files in This Item:
Thumbnail

  • File : TNS06114.pdf
  • Description : 
  • Size : 705.28 kB
  • Format : Adobe PDF


  • Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.