Joseph, KT and Sachdev, PL (2001) Initial boundary value problems for scalar and vector burgers equations. In: Studies in Applied Mathematics, 106 (4). pp. 481505.

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Abstract
In this article we study Burgers equation and vector Burgers equation with initial and boundry conditions. First we consider the Burgers equation in the quarter plane x > 0, t > 0 with Riemann type of initial and boundary conditions and use the HOPfcole transformation to linearize the problems and explicitily solve them. We study two limits, the small viscosity limit and the large time behaviour of solutions. Next, we study the vector Burgers equation and solve the initial value problem for it when the initial data are gredient of a scalar function. We investigate the asymptonic behaviour of this solution as time tends to infinity and generalize a rsult of HOPf to the vector case. Then we construct the exact Nwave solution as an asymptote of solution of an intitial value problem etending the previous work of Sachdev et al. (1994). We also study the limits as viscosity parameter goes to 0. Finally, we get an explicit solution for boundry value problem in a cylinder.
Item Type:  Journal Article 

Publication:  Studies in Applied Mathematics 
Publisher:  Blackwell Publishers 
Additional Information:  Copyright for this article belongs to Blackwell Publishers. 
Department/Centre:  Division of Physical & Mathematical Sciences > Mathematics 
Date Deposited:  15 Sep 2004 
Last Modified:  19 Sep 2010 04:16 
URI:  http://eprints.iisc.ac.in/id/eprint/1934 
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