Volume 7, Issue 2
Coercivity of the Single Layer Heat Potential

Douglas N. Arnold & Patrick J. Noon

DOI:

J. Comp. Math., 7 (1989), pp. 100-104

Published online: 1989-07

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  • Abstract

The single layer heat potential optential operator, K, arises in the solution of initialboundary 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 covercivity 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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@Article{JCM-7-100, author = {}, title = {Coercivity of the Single Layer Heat Potential}, journal = {Journal of Computational Mathematics}, year = {1989}, volume = {7}, number = {2}, pages = {100--104}, abstract = { The single layer heat potential optential operator, K, arises in the solution of initialboundary 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 covercivity 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9459.html} }
TY - JOUR T1 - Coercivity of the Single Layer Heat Potential JO - Journal of Computational Mathematics VL - 2 SP - 100 EP - 104 PY - 1989 DA - 1989/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9459.html KW - AB - The single layer heat potential optential operator, K, arises in the solution of initialboundary 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 covercivity 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.
Douglas N. Arnold & Patrick J. Noon. (1970). Coercivity of the Single Layer Heat Potential. Journal of Computational Mathematics. 7 (2). 100-104. doi:
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