This paper concerns the separable solutions of a generalized Burgers equation. Existence of separable solutions to the generalized Burgers equation is proved under certain conditions. A careful numerical study shows that these separable solutions of the generalized Burgers equation describe the large time asymptotic behavior of solutions of initial boundary value problems. © 2015 Wiley Periodicals, Inc., A Wiley Company.

Chidella Srinivasa Rao

Department of Mathematics

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Studies in Applied Mathematics

In this paper, we discuss the large-time asymptotics for periodic solutions of a generalized Burgers equation with variable viscosity (GBEV). Large-time asymptotics for the solutions of the GBEV depend on the parameters present in the partial differential equation and also the period of the solution of the GBEV. Large-time asymptotic expansions of the solutions are obtained by improving the solution of the linearized GBEV for certain parametric regionsviaa perturbative approach. These constructed large-time asymptotics are compared with the corresponding numerical solutions and are found to be in good agreement for large time. For certain other parametric region, our numerical study suggests that the solution of the inviscid GBEV describes the large-time behavior of the periodic solutions of the GBEV. © 2011 by the Massachusetts Institute of Technology.

Large-time asymptotics for solutions of a generalized Burgers equation with variable viscosity

Self-Similarity and Beyond

Advanced Mathematical Methods for Scientists and Engineers I

Journal of Mathematical Analysis and Applications

Classification of Self Similar Solutions to a Generalized Burgers Equation

SIAM Journal on Numerical Analysis

Godunov-Mixed Methods for Advective Flow Problems in One Space Dimension

A study of separable solutions of a generalized burgers equation

Journal	Studies in Applied Mathematics
Publisher	Blackwell Publishing Ltd
ISSN	00222526
Open Access	No