Application of the functional calculus to solving of infinite dimensional heat equation

In this paper we study infinite dimensional heat equation associated with the Gross Laplacian. Using the functional calculus method, we obtain the solution of appropriate Cauchy problem in the space of polynomial ultradifferentiable functions. The semigroup approach is considered as well.

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Bibliographic Details
Published in:	Karpats'kì matematinì publìkacìï Vol. 8; no. 2; pp. 313 - 322
Main Author:	Sharyn, S.V.
Format:	Journal Article
Language:	English
Published:	Vasyl Stefanyk Precarpathian National University 30.12.2016
Subjects:	gross laplacian infinite dimensional heat equation space of polynomial ultradifferentiable functions space of polynomial ultradistributions
ISSN:	2075-9827, 2313-0210
Online Access:	Get full text
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Description
Summary:	In this paper we study infinite dimensional heat equation associated with the Gross Laplacian. Using the functional calculus method, we obtain the solution of appropriate Cauchy problem in the space of polynomial ultradifferentiable functions. The semigroup approach is considered as well.
ISSN:	2075-9827 2313-0210
DOI:	10.15330/cmp.8.2.313-322