Azerbaijan National Academy of Science

Azerbaijan scientists's article is published in an authoritative international journal with the higher impact factor  “Differential Equations” of “Web of Science” international database. 

The authors of the work “Well-Posed Solvability of the Neumann Problem for a Generalized Mangeron Equation with Nonsmooth Coefficients”, published under a grant of ANAS Presidium, Director of the Institute of Mathematics and Mechanics, corresponding member of ANAS, Professor  Misir Mardanov, head of the laboratory “Mathematical problems of control” of ANAS Institute of Control Systems, Professor of ANAS Ilgar Mammadov and the staff of the Institute of Mathematics and Mechanics – Professor Telman Malikov,  Professor of ANAS  Rovshan Bandaliev. 

In the article for the fourth-order generalized Mangeron equation with nonsmooth coefficients, defined on a rectangular domain, the Neumann problem with non-classical conditions that do not require matching conditions is considered. The equivalence of these conditions to classical boundary conditions is justified if a solution to the problem is sought in the Sobolev isotropic space. The solution is carried out by reduction to a system of integral equations, the correct solvability of which is established on the basis of the method of integral representations. The correct solvability of the Neumann problem for the generalized Mangeron equation is proved by the method of operator equations.

We emphasize that in the literature so far the Neumann problem for the generalized Mangeron equation has been studied only for the case of sufficiently smooth coefficients. In this work, the Neumann problem for the generalized Mangeron equation is the first investigated under more natural conditions on the coefficients of the equation. In addition, the considered generalized Mangeron equation is a generalization of many model equations of various physical processes (Boussinesq-Love equation, generalized moisture transfer equation, telegraph equation, string vibration equation, heat equation, Aller equation, etc.). Thus, the considered problem has not only theoretical, but also great practical interest.

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