# 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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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.