A noncharacteristic Cauchy problem for a one-dimensional linear parabolic equation with coefficients depending on the time is studied. In general, the solutions of the problem do not depend continuously on the Cauchy data. However, it is proved in the paper that solutions that are bounded in the supremum norm depend continuously on the Cauchy data. Furthermore, several stability estimates characterizing this continuity are established. Similar results are also obtained for regular level lines of such solutions.
Stability results for solutions of a linear parabolic noncharacteristic Cauchy problem / E. Francini. - In: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. - ISSN 0928-0219. - STAMPA. - 8:(2000), pp. 255-272. [10.1515/jiip.2000.8.3.255]
Stability results for solutions of a linear parabolic noncharacteristic Cauchy problem
FRANCINI, ELISA
2000
Abstract
A noncharacteristic Cauchy problem for a one-dimensional linear parabolic equation with coefficients depending on the time is studied. In general, the solutions of the problem do not depend continuously on the Cauchy data. However, it is proved in the paper that solutions that are bounded in the supremum norm depend continuously on the Cauchy data. Furthermore, several stability estimates characterizing this continuity are established. Similar results are also obtained for regular level lines of such solutions.File | Dimensione | Formato | |
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