IJPAM: Volume 10, No. 3 (2004)

SERIES OF POLYNOMIAL SOLUTIONS FOR
A CLASS OF EVOLUTION EQUATIONS

Gerald N. Hile$^{1}$, Alexander Stanoyevitch$^{2}$
$^{1}$Department of Mathematics
University of Hawaii at Manoa
Honolulu, Hawaii 96822, USA
email: hile@hawaii.edu
$^{2}$Department of Mathematics
University of Guam
UOG Guam Station, Mangilao, GU, USA
email: alex@math.hawaii.edu


Abstract.We derive pointwise upper bounds on generalized heat polynomials for a class of higher order linear homogeneous evolution equations. These bounds are analogous to those of Rosenbloom and Widder on the heat polynomials, and lead to estimates on the width of the strip of convergence of series expansions in terms of these polynomial solutions. For a subclass of equations including the heat equation, the estimates give the exact width of the strip of convergence. An application is given to a Cauchy problem, wherein the solution is expressed as the sum of a series of polynomial solutions, provided that the Cauchy data is analytic and obeys a growth condition at infinity related to bounds on the coefficients of the differential equation.

Received: November 2, 2003

AMS Subject Classification: 35C10, 35K25, 35C05, 35K30

Key Words and Phrases: heat polynomials, polynomial solutions, evolution equations, series expansions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 10
Issue: 3