Mathematical Problems in Engineering 
Volume 7 (2001), Issue 3, Pages 253-282
doi:10.1155/S1024123X01001648

Analysis of the self-similar solutions of a generalized Burger's equation with nonlinear damping

Ch. Srinivasa Rao,1 P. L. Sachdev,1 and Mythily Ramaswamy2

 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

Abstract

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.