An explicit stability estimate for an ill-posed Cauchy problem for the wave equation

An explicit stability estimate for the two-dimensional wave equation when the Cauchy data are prescribed on a part of the lateral boundary is derived. Our result is obtained using a combination of the Friedrichs-Leray energy integrals and Carleman type estimates of Hörmander [“Linear Partial Differe...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 156; no. 2; pp. 597 - 610
Main Authors Ames, K.A, Isakov, Victor
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.1991
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Summary:An explicit stability estimate for the two-dimensional wave equation when the Cauchy data are prescribed on a part of the lateral boundary is derived. Our result is obtained using a combination of the Friedrichs-Leray energy integrals and Carleman type estimates of Hörmander [“Linear Partial Differential Operators,” Springer-Verlag, New York/Berlin, 1976]. Since the calculation of explicit constants produces a number of difficulties, this general approach is modified in several ways, e.g., the introduction of a set of special constraints. Such results are useful in constructing algorithms that generate numerical solutions to these kinds of ill-posed problems.
ISSN:0022-247X
1096-0813
DOI:10.1016/0022-247X(91)90417-X