Abstract
The work is devoted to study the existence and uniqueness of the classical solution of the inverse boundary value problem of determining the lowest coefficient in one fourth order equation. The original problem is reduced to an equivalent problem. The existence and uniqueness of the integral equation are proved by means of the contraction mappings principle, and we obtained that this solution is unique for a boundary value problem. Further, using these facts, we prove the existence and uniqueness of the classical solution for this problem.
Highlights
Modern problems of natural science lead to study qualitatively new problems, a vivid example of which is the class of nonlocal problems for partial differential equations
Among non-local problems, of great interest are problems with integral conditions. Such integral conditions appear in the mathematical modeling of phenomena associated with a physical plasma [18], the spread of heat [2, 6], and the process of moisture transfer in capillary-simple media [7], issues of demography and mathematical biology, as well as in the study of some inverse problems of mathematical physics
Questions of solvability of problems with non-local integral conditions for partial differential equations are studied in the papers [4, 8, 11]
Summary
Modern problems of natural science lead to study qualitatively new problems, a vivid example of which is the class of nonlocal problems for partial differential equations. Questions of solvability of problems with non-local integral conditions for partial differential equations are studied in the papers [4, 8, 11]. Inverse problems with an integral redefinition condition for partial differential equations were studied in [5, 9, 13,14,15,16,17].
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