Abstract
We study slowly moving viscous shock associated with the Burgers equation defined in the quarter plane ubject to the constant input data. The true splution for the given problem is derived by using the classical Cole-Hopf transformation and the Robin function of the resultant problem, and is written in terms of the complementary error function and its first iterated integral. A viscous shocj structure is botained by analyzing the asymptotic behavior of the true solution for small viscosity and is expressed in terms of the hyperbolic tangent function. The obtained viscous shocj is not of the form that one might expect a Pariori. The location of the viscous shock, which is governed by a nonlin ear algebraic equation, is solved by using the Lambert W function. A full charactrization of shock location and shock speed is shown.
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