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arXiv:1609.01890 [math.AP]AbstractReferencesReviewsResources

On recovering parabolic diffusions from their time-averages

Nikolai Dokuchaev

Published 2016-09-07Version 1

The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a prescribed time-average of the solution. It is shown that this new problem is well-posed. The paper establishes existence, uniqueness, and a regularity of the solution for this new problem and its modifications, including problems with singled out terminal values.

Categories: math.AP
Subjects: 35K20, 35Q99, 32A35
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