Large time asymptotics for solutions to a nonhomogeneous Burgers equation

• Published in: Applied mathematics and mechanics Vol. 31; no. 9; pp. 1189 - 1196
• Main Authors: Chidella, S. R., Yadav, M. K.
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.09.2010; Department of Mathematics,Indian Institute of Technology Madras,Chennai 600036,India
• Subjects: Applications of Mathematics; Asymptotic properties; Burgers equation; Classical Mechanics; Decay; Fluid- and Aerodynamics; Heat equations; Initial value problems; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Self-similarity; Series (mathematics); 35C06; nonhomogeneous Burgers equation; 35K15; Hermite polynomials; 35B40; self-similar solutions; 35K55; O175.2
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-010-1352-9

In this article, the solutions to a nonhomogeneous Burgers equation subject to bounded and compactly supported initial profiles are constructed. In an interesting study, Kloosterziel （Journal of Engineering Mathematics 24, 213-236 （1990）） represented a solution to an initial value problem （IVP） for the heat equation, with an initial data in a class of rapidly decaying functions, as a series of self-similar solutions to the heat equation. This approach quickly revealed the large time behaviour for the solution to the IVP. Inspired by Kloosterziel＇s approach, the solution to the nonhomogeneous Burgers equation is expressed in terms of the self-similar solutions to the heat equation. The large time behaviour of the solutions to the nonhomogeneous Burgers equation is obtained.