The Large‐Time Solution of Burgers' Equation with Time‐Dependent Coefficients. I. The Coefficients Are Exponential Functions
In this paper, we consider an initial‐value problem for Burgers' equation with variable coefficients
x and t represent dimensionless distance and time, respectively, and ,
are given functions of t. In particular, we consider the case when the initial data have algebraic decay as , with
The constant states
and are problem parameters. Two specific initial‐value problems are considered.
In initial‐value problem 1 we consider the case when
while in initial‐value problem 2 we consider the case when
The method of matched asymptotic coordinate expansions is used to obtain the large‐t asymptotic structure of the solution to both initial‐value problems over all parameter values.
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Document Type: Research Article
Publication date: February 1, 2016