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

doi:10.1016/S0252-9602(14)60096-5

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1461-1472.doi: 10.1016/S0252-9602(14)60096-5

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

Manoj K. YADAV

Department of Mathematics, Indian Institute of Science, Bangalore 560012, India

收稿日期:2013-04-15 修回日期:2014-04-13 出版日期:2014-09-20 发布日期:2014-09-20
基金资助:
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)).

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

Manoj K. YADAV

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)).

摘要/Abstract

摘要：

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⁻¹e^β|x|^2/2, β ≥ 0, x ∈ 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.

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

Abstract:

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

中图分类号:

33C45

Manoj K. YADAV. SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS[J]. 数学物理学报(英文版), 2014, 34(5): 1461-1472.

Manoj K. YADAV. SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS[J]. Acta mathematica scientia,Series B, 2014, 34(5): 1461-1472.

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

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

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