Advanced Search
Article Contents
Article Contents

Mean periodic solutions of a inhomogeneous heat equation with random coefficients

  • * Corresponding author

    * Corresponding author 

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

Abstract Full Text(HTML) Related Papers Cited by
  • 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.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] H. Amann, Periodic solutions for semi-linear parabolic equations, in Nonlinear Analysis: A Collection of Papers in Honor of Erich Rothe, Academic Press, (1978), 1–29.
    [2] N. Hirano, Existence of multiple periodic solutions for a semilinear evolution equations, Proc. Amer. Math. Soc., 106 (1989), 107-114.  doi: 10.1090/S0002-9939-1989-0953007-5.
    [3] R. Z. Khasminskii, Ustoychivost' Sistem Differencial'nyh Uravnenii pri Sluchainykh Vozmushcheniyakh ikh Parametrov, (Russian) [Stability of Systems of Differential Equations under Random Perturbations of Their Parameters], Nauka, Moscow, 1969.
    [4] Yu. S. Kolesov, O nekotorykh priznakakh sushchestvovaniya ustoichivykh periodicheskikh reshenii u kvasilineinykh parabolicheskikh uravnenii, (Russian) [Some of the signs of existence of stable periodic solutions for quasilinear parabolic equations], Dokl. AN SSSR, 157 (1964), 1288-1290. 
    [5] I. I. Shmulev, Periodicheskie resheniya pervoi kraevoi zadachi dlya parabolicheskikh uravnenii, (Russian) [Periodic solutions of the first boundary problem for pabolic equations], Matem. sb., 66 (1965), 398-410. 
    [6] A. N. Tikhonov and A. A. Samarskii, Uravneniya Matematičesko$\check{i}$ Fiziki, (Russian) [Equations of Mathematical Physics], Nauka, Moscow, 1953.
    [7] V. A. Yakubovich and V. M. Starzhinskii, Lineinye Differencial'nye Uravneniya s Periodicheskimi Koefficientami i ikh Prilozheniya, (Russian) [Linear Differential Equations with Periodic Coefficients and Their Applications], Nauka, Moscow, 1972.
    [8] V. G. Zadorozhniy, Metody Variatsionnogo Analiza, (Russian) [Methods of Variational Analysis], NIC "Regulyarnaya i Khaoticheskaya Dinamika", Institut Kompyuternyh Issledovanii, Moscow-Izhevsk, 2006.
    [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.
  • 加载中

Article Metrics

HTML views(516) PDF downloads(216) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint