Open AccessNonlocal integro-differential problems of multi-dimensional wave processes
Author(s) -
Н. С. Попов
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1268/1/012060
Subject(s) - mathematics , boundary value problem , uniqueness , mathematical analysis , continuation , regularization (linguistics) , differential equation , integral equation , computer science , artificial intelligence , programming language
Nonlocal boundary-value problems for one-dimensional parabolic second-order equations with integral conditions on the lateral boundary are considered in the articles by A.I. Kozhanov. Higher-dimensional integro–differential equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability. In the present article we study integro-differential equations with integral conditions on the lateral boundary and prove existence theorems for regular solutions.