Mean periodic solutions of a inhomogeneous heat equation with random coefficients

Galina Kurina; Vladimir Zadorozhniy

doi:10.3934/dcdss.2020087

Article Contents

2020, Volume 13, Issue 5: 1543-1551. Doi: 10.3934/dcdss.2020087

This issue Previous Article Vector-valued Schrödinger operators in L^p-spaces Next Article The Stokes problem in fractal domains: Asymptotic behaviour of the solutions

Mean periodic solutions of a inhomogeneous heat equation with random coefficients

Galina Kurina^1,2,3, , and
Vladimir Zadorozhniy^1,

1.
Voronezh State University, Universitetskaya pl., 1, Voronezh, 394018, Russia
2.
Institute of Law and Economics, Leninskii pr., 119-A, Voronezh, 394042, Russia
3.
Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Vavilova ul., 44/2, Moscow, 119333, Russia

^* Corresponding author
^* Corresponding author

Received: January 31, 2018

Revised: August 31, 2018

Published: March 2020

The first author is supported by the Russian Science Foundation project No. 17-11-01220

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Abstract

We present conditions ensuring the periodicity of the mathematical expectation of a solution of a scalar linear inhomogeneous heat equation with random coefficients where the coefficient in front of the unknown functions is Gaussian or it is uniformly distributed. The obtained results may be treated as finding a control ensuring the periodicity of the mathematical expectation of a solution of the heat equation.

Keywords:

Heat equation,
random coefficients,
periodicity of mathematical expectation.

Mathematics Subject Classification: Primary: 35K05, 35R60.

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References

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