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The large-time solution of a nonlinear fourth-order equation initial-value problem I. Initial data with a discontinuous expansive step

Citation

Leach, JA and Bassom, AP, The large-time solution of a nonlinear fourth-order equation initial-value problem I. Initial data with a discontinuous expansive step, The ANZIAM Journal, 51, (2) pp. 178-190. ISSN 1446-1811 (2009) [Refereed Article]

Copyright Statement

Copyright Australian Mathematical Society 2010

DOI: doi:10.1017/S1446181110000015

Abstract

In this paper we consider an initial-value problem for the nonlinear fourth-order partial differential equation ut+uux+γuxxxx=0, −<x<, t>0, where x and t represent dimensionless distance and time respectively and γ is a negative constant. In particular, we consider the case when the initial data has a discontinuous expansive step so that u(x,0)=u0(>0) for x≥0 and u(x,0)=0 for x<0. The method of matched asymptotic expansions is used to obtain the large-time asymptotic structure of the solution to this problem which exhibits the formation of an expansion wave. Whilst most physical applications of this type of equation have γ>0, our calculations show how it is possible to infer the large-time structure of a whole family of solutions for a range of related equations.

Item Details

Item Type:Refereed Article
Keywords:partial differential equation, asymptotic analysis
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:105714
Year Published:2009
Deposited By:Mathematics and Physics
Deposited On:2016-01-13
Last Modified:2016-11-25
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