WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
On the Solvability of One Inverse Boundary Value Problem of Recovering Unknown coefficients and the Right-Hand Side in a Fourth-Order Pseudohyperbolic Equation
Authors: , ,
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Abstract: We study the classical solution of the nonlinear inverse boundary value problem for a pseudo-hyperbolic equation of the fourth order. The essence of the problem is that it is required, together with the solution, to determine the unknown coefficient. The problem is considered in a rectangular area. To solve the considered problem, the transition from the original inverse problem to an auxiliary inverse problem is carried out. The existence and uniqueness of a solution to the auxiliary problem are proved with the help of contracted mappings. Then the transition to the original inverse problem is made, and as a result, a conclusion is made about the solvability of the original inverse problem.
Keywords:
Inverse boundary problem, pseudo-hyperbolic equation, Fourier method, classic solution, integral overdetermination condition, existence and uniqueness, nonlocal integral condition, functional analysis, differential equations, mathematical modelling
Pages: 274-286
DOI: 10.37394/23206.2026.25.28