MEAN PERIODIC SOLUTIONS OF A INHOMOGENEOUS HEAT EQUATION WITH RANDOM COEFFICIENTS

被引：0

作者：

Kurina, Galina ^{[1
,2
,3
]}

Zadorozhniy, Vladimir ^{[1
]}

机构：

[1] Voronezh State Univ, Univ Skaya Pl 1, Voronezh 394018, Russia

[2] Inst Law & Econ, Leninskii Pr 119-A, Voronezh 394042, Russia

[3] Russian Acad Sci, Fed Res Ctr Comp Sci & Control, Vavilova Ul 44-2, Moscow 119333, Russia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2020年 / 13卷 / 05期

基金：

俄罗斯科学基金会;

关键词：

Heat equation; random coefficients; periodicity of mathematical expectation; EXISTENCE;

D O I：

10.3934/dcdss.2020087

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1543 / 1551

页数：9

共 10 条

[1]

Amann H., 1978, Nonlinear Analysis: A Collection of Papers in Honor of Erich H. Rothe, DOI [10.1016/b978-0-12-165550-1.50007-0, DOI 10.1016/B978-0-12-165550-1.50007-0]

[2] EXISTENCE OF MULTIPLE PERIODIC-SOLUTIONS FOR A SEMILINEAR EVOLUTION EQUATION [J].

HIRANO, N .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 106 (01) :107-114

[3]

Khasminskii R. Z., 1969, USTOYCHIVOST SISTEM

[4]

KOLESOV YS, 1964, DOKL AKAD NAUK SSSR+, V157, P1288

[5]

Shmulev I. I., 1965, MAT SBORNIK, V66, P398

[6]

TIKHONOV AN, 1953, URAVNENIYA MATEMATIC

[7]

Yakubovich V. A., 1972, LINEINYE DIFFERENCIA

[8] Mean periodic solutions of a linear inhomogeneous first-order differential equation with random coefficients [J].

Zadorozhniy, V. G. ;

Kurina, G. A. .

DIFFERENTIAL EQUATIONS, 2014, 50 (06) :722-741

[9] Mean-Periodic Solutions of a First-Order Linear Differential Equation [J].

Zadorozhniy, V. G. ;

Kurina, G. A. .

DOKLADY MATHEMATICS, 2013, 87 (03) :325-330

[10]

Zadorozhniy V. G., 2006, METODY VARIATSIONNOG

← 1 →