Year: 1989
Journal of Computational Mathematics, Vol. 7 (1989), Iss. 2 : pp. 100–104
Abstract
The single layer heat potential operator, K, arises in the solution of initial-boundary value problems for the heat equation using boundary integral methods. In this note we show that K maps a certain anisotropic Sobolev space isomorphically onto its dual, and, moreover, satisfies the coercivity inequality $ < K_{q,q} >\geq c\|q\|^2$. We thereby establish the well-posedness of the operator equation $K_q=f$ and provide a basis for the analysis of the discretizations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1989-JCM-9459
Journal of Computational Mathematics, Vol. 7 (1989), Iss. 2 : pp. 100–104
Published online: 1989-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 5