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Continuous dependence on geometry for the backward heat equation
Author(s) -
Crooke P. S.,
Payne L. E.
Publication year - 1984
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670060126
Subject(s) - mathematics , domain (mathematical analysis) , boundary value problem , geometry , heat equation , constraint (computer aided design) , boundary (topology) , mathematical analysis
In this paper we are concerned with the development of criteria for stabilizing inherently unstable initial‐boundary value problems under small errors in the geometry of the underlying domain. We consider in particular the initial‐boundary‐value problem for the backward heat equation assuming that some error has been made in characterizing the geometry of the domain under consideration. It is shown that solutions which belong to an appropriately defined constraint set depend continuously in L 2 on errors in the geometry.