BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, SOBOLEV-TYPE EQUATIONS WITH UNKNOWN RIGHT SIDE // BSU Bulletin. Mathematics, Informatics. - 2021. №4. . - С. 34-47.
Title:
SOBOLEV-TYPE EQUATIONS WITH UNKNOWN RIGHT SIDE
Financing:
Работа выполнена в рамках государственного задания ИМ СО РАН, проект 0314-2019-0010.
Codes:
Annotation:
The work is devoted to the study of the solvability of inverse problems of finding, together with the solution of some Sobolev-type equations, also an unknown right-hand side (unknown external sources). The peculiarity of the studied problems is that the desired right part in them is determined by an unknown multiplier that depends only on spatial variables. The research method in the work is based on the transition from the inverse problem to a new direct problem for equations of a composite type. For the problems under study, the theorems of the existence and uniqueness of regular solutions are proved in the work - solutions having all derivatives generalized by S. L. Sobolev included in the corresponding equation.
Keywords:
differential equations of Sobolev type, inverse problems, unknown right side, regular solutions, existence, uniqueness.
List of references:
Article.pdf