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Analysis of the self-similar solutions of a generalized Burgers equation with nonlinear damping

Rao, Srinivasa and Sachdev, PL and Ramaswamy, Mythily (2001) Analysis of the self-similar solutions of a generalized Burgers equation with nonlinear damping. In: Mathemafical Problems in Engineering, 7 (3). 253-282..

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Abstract

The object of investigation in this paper is a nonlinear ordinary differential equation obtained by means of self-similar reduction of the generalized Burgers equation $u_t+u^\beta u_x+\lambda u^\alpha=\delta u_{xx}$ with the nonlinear damping term $\lambda u^\alpha$. More exactly, the authors study the initial value problem $g"+2\eta g'+2\beta^{-1}g-2^{3/2}g^\beta g'-4\lambda g^\alpha=0$, $g(0)=\nu$, $g'(0)=0$ by using both numerical and analytical methods. Here $\alpha>0$, $\beta=(\alpha-1)/2>0$, $\lambda$, $\delta>0$ and $\nu >0$ are constants. Existence of positive bounded solutions with exponential and algebraic types of decay to zero at infinity is proved for special ranges of parameters.

Item Type: Journal Article
Additional Information: copyright of this article belongs to OPA (Ovemas Publishers Association) N.V.
Keywords: Burgers equations;Initial value problem;Generalized burgers equation;Self similar solutions
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 15 Oct 2007
Last Modified: 19 Sep 2010 04:39
URI: http://eprints.iisc.ernet.in/id/eprint/11872

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