An interesting case of variables separation
type: Item
instance of: scholarly article
title: An interesting case of variables separation
zbMATH Open document ID: 0973.35049
DOI: 10.1016/S0893-9659(00)00030-6
author: R. Smith
published in: Applied Mathematics Letters
publication date: 2000-11-16T00:00:00Z
review text: There is an application of holomorphic expansions \[ W= \sum^\infty_{|n|= 0}\overline z^n W_n(z)\tag{HE} \] and connected results to construct explicit solution for linear partial differential equation (PDE) with constant coefficients, as for instance heat, wave or Laplace equations. The method consist of writing the complex analog of PDE and search for a solution in form of an (HE) with unknown coefficients \(W_n(z)\). The theoretical justification for this technique is done. As an example, a particular solution for a nonhomogeneous wave equation is computed.
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35E20
zbMATH DE Number: 1531176
zbMATH Keywords: holomorphic expansions
zbMATH Keywords: Laplace equations
zbMATH Keywords: nonhomogeneous wave equation
reviewed by: Claudia Simionescu-Badea
MaRDI profile type: Publication
cites work: Q5582453
cites work: Q4109994
cites work: A function theory for finding a basis for all polynomial solutions to linear constant coefficient pde's of homogeneous order
Wikidata QID: Q127932663
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description: scientific article; zbMATH DE number 1531176