Boundary Value Problems for Burgers Equations, through Nonstandard Analysis

DOI: 10.4236/am.2015.66099   PDF   HTML   XML   3,613 Downloads   4,207 Views   Citations


In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane . First we consider the Burgers equations with initial conditions admitting two and three shocks and use the HOPF-COLE transformation to linearize the problems and explicitly solve them. Next we study the Burgers equation and solve the initial value problem for it. We study the asymptotic behavior of solutions and we show that the exact solution of boundary value problem for viscid Burgers equation as viscosity parameter is sufficiently small approach the shock type solution of boundary value problem for inviscid Burgers equation. We discuss both confluence and interacting shocks. In this article a new approach has been developed to find the exact solutions. The results are formulated in classical mathematics and proved with infinitesimal technique of non standard analysis.

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Bendaas, S. (2015) Boundary Value Problems for Burgers Equations, through Nonstandard Analysis. Applied Mathematics, 6, 1086-1098. doi: 10.4236/am.2015.66099.

Conflicts of Interest

The authors declare no conflicts of interest.


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