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｜2/2,β ≥ 0, x ∈ Rn. This linear ...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｜2/2,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＆gt;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.展开更多
基金supported by Research Grants of National Board for Higher Mathematics(Award No:2/40(13)/2010-R&D-II/8911)UGC’s Dr.D.S.Kothari Fellowship(Award No.F.4-2/2006(BSR)/13-440/2011(BSR))
文摘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｜2/2,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＆gt;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.
