Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 64, pp. 1-25.

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

Authors: G. N. Hile (Univ. of Hawaii, Honolulu, Hawaii, USA)
         Alexander Stanoyevitch (Univ. of Guam, Mangilao, GU, USA)
         
Abstract: 
  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.