Geodesic
Expansions of solutions of higher order evolution equations in series of generalized heat polynomials
Electronic journal of differential equations, Tome 2002 (2002)
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.
Classification : 35C10, 35K25, 35C05, 35K30
Keywords: heat polynomials, polynomial solutions, evolution equations, series expansions 
@article{EJDE_2002__2002__a270,
     author = {Hile,  G.N. and Stanoyevitch,  Alexander},
     title = {Expansions of solutions of higher order evolution equations in series of generalized heat polynomials},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1003.35036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a270/}
}
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%A Stanoyevitch,  Alexander
%T Expansions of solutions of higher order evolution equations in series of generalized heat polynomials
%J Electronic journal of differential equations
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Hile,  G.N.; Stanoyevitch,  Alexander. Expansions of solutions of higher order evolution equations in series of generalized heat polynomials. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a270/