On recovering parabolic diffusions from their time-averages
Citation
Dokuchaev, N. 2019. On recovering parabolic diffusions from their time-averages. Calculus of Variations and Partial Differential Equations. 58: Article ID 27.
Source Title
Calculus of Variations and Partial Differential Equations
ISSN
Faculty
Faculty of Science and Engineering
School
School of Electrical Engineering, Computer and Mathematics Science (EECMS)
Remarks
The final publication is available at Springer via http://dx.doi.org/10.1007/s00526-018-1464-1
Collection
Abstract
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 in certain classes of solutions. 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.
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