Large Time Asymptotics for Solutions of a Nonhomogeneous Burgers Equation

Ch. Srinivasa Rao; Manoj K Yadav

doi:10.3879/j.issn.1000-0887.2010.09.012

Volume 31 Issue 9

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Ch. Srinivasa Rao, Manoj K Yadav. Large Time Asymptotics for Solutions of a Nonhomogeneous Burgers Equation[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1133-1139. doi: 10.3879/j.issn.1000-0887.2010.09.012

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Large Time Asymptotics for Solutions of a Nonhomogeneous Burgers Equation

doi: 10.3879/j.issn.1000-0887.2010.09.012

Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India

Received Date: 1900-01-01
Rev Recd Date: 2010-06-04
Publish Date: 2010-09-15

Abstract

Abstract

Solutions of a nonhomogeneous Burgers equation subject to bounded and compactly supported initial profiles were constructed.In an interesting study,Kloosterziel(Kloosterziel R C.J Engrg Math,1990, 24(3):213-236)represented the solution of an initial value problem(IVP)for the heat equation,with initial data in(L²(R,e^x²/2),as a series of the self-similar solutions of the heat equation.This approach quickly revealed the large time behaviour for the solution of the IVP.Inspired by Kloosterziel's approach, the solution of the nonhomogeneous Burgers equation in terms of the self-similar solutions of the heat equation was expressed.Finally,the large time behaviour of the solutions of the nonhomogeneous Burgers equation is obtained.
- nonhomogeneous Burgers equation,
- Hermite polynomials,
- self-similar solutions

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References(10)

References

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