Electron. J. Diff. Eqns., Vol. 2003(2003), No. 87, pp. 1-64.

The generalized Airy diffusion equation

Frank M. Cholewinski & James A. Reneke

Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.

Submitted February 3, 2003. Published August 22, 2003.
Math Subject Classifications: 33C10, 35C05, 44A15.
Key Words: Diffusion polynomial solutions, Bessel calculus, positive definite kernels.

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Frank M. Cholewinski
Department of Mthematical Sciences
Clemson University
Clemson, SC 29634, USA
email: cholewa@innova.net
James A. Reneke
Department of Mathematical Sciences
Clemson University
Clemson, SC 29634, USA
email: reneke@ces.clemson.edu

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