Mathematical Problems in Engineering
Volume 7 (2001), Issue 3, Pages 253-282
Analysis of the self-similar solutions of a generalized
Burger's equation with nonlinear damping
1Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
2TIFR Centre, Indian Institute of Science, Bangalore 560 012, India
Received 27 November 2000
Copyright © 2001 Ch. Srinivasa Rao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming initial conditions at the origin we observe a wide variety of solutions – (positive) single hump, unbounded or those with a finite zero. The existence and nonexistence of positive bounded solutions with different types of decay (exponential or algebraic) to zero at infinity for specific parameter ranges are proved.