Rao, Srinivasa and Sachdev, PL and Ramaswamy, Mythily (2001) Analysis of the selfsimilar solutions of a generalized Burgers equation with nonlinear damping. In: Mathemafical Problems in Engineering, 7 (3). 253282..

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Abstract
The object of investigation in this paper is a nonlinear ordinary differential equation obtained by means of selfsimilar 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 $g"+2\eta g'+2\beta^{1}g2^{3/2}g^\beta g'4\lambda g^\alpha=0$, $g(0)=\nu$, $g'(0)=0$ by using both numerical and analytical methods. Here $\alpha>0$, $\beta=(\alpha1)/2>0$, $\lambda$, $\delta>0$ 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 

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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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