Linear inverse problems for the heat equation and non-local boundary value problems with generalized Samarskii–Ionkin condition

被引：0
|
作者：
A. I. Kozhanov
T. N. Shipina
机构：
[1] Sobolev Institute of Mathematics,
[2] Siberian Federal University,undefined
来源：
Boletín de la Sociedad Matemática Mexicana | 2023年 / 29卷
关键词：
Heat equation; Linear inverse problems; Generalized Samarskii–Ionkin condition; Regular solutions; Existence and uniqueness.; 35R30; 35K20;
D O I：
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学科分类号：
摘要：
The paper is devoted to the study of the solvability of linear inverse problems for a one-dimensional heat equation with an unknown right-hand side. The aim of the work is to obtain theorems of the existence and uniqueness of regular solutions (i.e., solutions having all weak derivatives in the sense of Sobolev occurring in the equation) The proofs will essentially use new results on the solvability of nonlocal problems with a generalized Samarskii–Ionkin boundary condition.
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