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Solutions of a Nonhomogeneous Burgers Equation
Published in
2010
Volume: 124
   
Issue: 4
Pages: 411 - 422
Abstract
In this article, we construct solutions of a nonhomogeneous Burgers equation subject to certain unbounded initial profiles. In an interesting study, Kloosterziel [1] represented the solution of an initial value problem (IVP) for the heat equation, with initial data in , as a series of the self-similar solutions of the heat equation. This approach quickly revealed the large time behavior for the solution of the IVP. Inspired by Kloosterziel [1]'s approach, we express the solution of the nonhomogeneous Burgers equation in terms of the self-similar solutions of a linear partial differential equation with variable coefficients. Finally, we also obtain the large time behavior of the solution of the nonhomogeneous Burgers equation. © 2010 by the Massachusetts Institute of Technology.
About the journal
JournalStudies in Applied Mathematics
ISSN00222526
Open AccessNo