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

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

Abstract

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⁻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.

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

CLC Number:

33C45

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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