On recovering parabolic diffusions from their time-averages

  • Nikolai Dokuchaev


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.

Mathematics Subject Classification

35K20 35Q99 32A35 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electrical Engineering, Computing and Mathematical SciencesCurtin UniversityPerthAustralia

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