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Initial boundary value problems for scalar and vector burgers equations

Joseph, KT and Sachdev, PL (2001) Initial boundary value problems for scalar and vector burgers equations. In: Studies in Applied Mathematics, 106 (4). pp. 481-505.


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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 HOPf-cole 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 N-wave 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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