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Mean periodic solutions of a inhomogeneous heat equation with random coefficients

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    * Corresponding author 

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

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  • 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.

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


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    [9] V. G. Zadorozhniy and G. A. Kurina, Periodicheskie v srednem resheniya lineinogo differencial'nogo uravneniya pervogo poryadka, (Russian) [Mean-periodic solutions of a first-order linear differential equation], Dokl. Akad. Nauk, 450 (2013), 505-510 (Engl. transl.: Dokl. Math., 87 (2013), 325-330.) doi: 10.1134/s1064562413030277.
    [10] V. G. Zadorozhniy and G. A. Kurina, Periodicheskie v srednem resheniya lineinogo neodnorodnogo differencial'nogo uravneniya pervogo poryadka so sluchainymi koefficientami, (Russian) [Mean periodic solutions of a linear inhomogeneous first-order differential equation with random coefficients], Differentcial'nye Uravneniya, 50 (2014), 726-744 (English transl.: Differential Equations, 50 (2014), 722-741.
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