On recovering parabolic diffusions from their time-averages

Dokuchaev, Nikolai

doi:10.1007/s00526-018-1464-1

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Access Status

Open access

Authors

Dokuchaev, Nikolai

Date

2019

Type

Journal Article

Metadata

Show full item record

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

DOI

10.1007/s00526-018-1464-1

ISSN

0944-2669

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

URI

http://hdl.handle.net/20.500.11937/75202

Collection

Curtin Research Publications

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.