Electron. J. Diff. Eqns., Vol. 2002(2002), No. 64, pp. 1-25.

Expansions of solutions of higher order evolution equations in series of generalized heat polynomials

G. N. Hile & Alexander Stanoyevitch

Upper bound estimates are established on generalized heat polynomials for higher order linear homogeneous evolution equations with coefficients depending on the time variable. These estimates are analogous to well known bounds of Rosenbloom and Widder on the heat polynomials. The bounds lead to further estimates on the width of the strip of convergence of series expansions in terms of these polynomial solutions. An application is given to a Cauchy problem, wherein the solution is expressed as the sum of a series of polynomial solutions.

Submitted January 22, 2002. Published July 11, 2002.
Math Subject Classifications: 35C10, 35K25, 35C05, 35K30.
Key Words: heat polynomials, polynomial solutions, evolution equations, series expansions.

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Gerald N. Hile
Department of Mathematics
University of Hawaii
Honolulu, HI 96822, USA
e-mail: hile@hawaii.edu
Alexander Stanoyevitch
Department of Mathematics
University of Guam
UOG Station, Mangilao, GU 96923, USA
e-mail: alex@math.hawaii.edu

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