A Singular Parabolic Initial-Boundary Value Problem in a Noncylindrical Domain

The well-posedness of the first Fourier problem for a class of singular parabolic equations in noncylindrical domain is established in an appropriate weighted Hilbert-Sobolev space. The Green's function is also constructed by means of potentials, and it is shown that the generalized and classic...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 1980-03, Vol.11 (2), p.348-357
Main Author: Alexiades, Vasilios
Format: Article
Language:English
Subjects:
Boundary value problems
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Summary:The well-posedness of the first Fourier problem for a class of singular parabolic equations in noncylindrical domain is established in an appropriate weighted Hilbert-Sobolev space. The Green's function is also constructed by means of potentials, and it is shown that the generalized and classical solutions coincide when the data permit the latter to exist.
ISSN:0036-1410
1095-7154
DOI:10.1137/0511032