Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (5): 1461-1472.doi: 10.1016/S0252-9602(14)60096-5

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SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

Manoj K. YADAV   

  1. Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
  • Received:2013-04-15 Revised:2014-04-13 Online:2014-09-20 Published:2014-09-20
  • Supported by:

    This work is supported by Research Grants of National Board for Higher Mathematics (Award No: 2/40(13)/2010-R&D-II/8911) and UGC´s Dr. D. S. Kothari Fellowship (Award No. F. 4-2/2006 (BSR)/13-440/2011(BSR)).

Abstract:

In this article, we obtain explicit solutions of a linear PDE subject to a class of ra-dial square integrable functions with a monotonically increasing weight function |x|n−1eβ|x|2/2β ≥ 0, ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in
terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.

Key words: forced Burgers equation, radial Hermite functions, generalized Laguerre poly-nomials, self-similar solutions

CLC Number: 

  • 33C45
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