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The work is devoted to the study of the solvability of the inverse boundary value problem with an unknown time depended coefficient for a sixth-order Boussinesq equation with an additional integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved. The sixth order Boussinesq-Type problem is discretized using the Quintic B-spline (QB-spline) collocation technique and reshaped as non-linear least-squares optimization of the Tikhonov regularization function. This is numerically solved by means of the MATLAB subroutine lsqnonlin tool. Both perturbed data and analytical solution are inverted. Numerical outcomes are reported and discussed. In addition, the von Neumann stability analysis for the proposed numerical approach has also been discussed. [ABSTRACT FROM AUTHOR]

This paper investigates the simultaneous identification of time-dependent lowest and source terms in a two-dimensional (2D) parabolic equation from the additional measurements. To investigate the solvability of the inverse problem, we first examine an auxiliary inverse boundary value problem and prove its equivalence to the original problem in a certain sense. Then, applying the contraction mappings principle existence and uniqueness of the solution of an equivalent problem is proved. Furthermore, using the equivalency, the existence and uniqueness theorem for the classical solution of the original problem is obtained and some discussions on the numerical solutions for this inverse problem are presented including numerical examples. [ABSTRACT FROM AUTHOR]

In this paper we study an inverse boundary value problem with an unknown time-dependent coefficient for a third-order pseudo-hyperbolic equation with an additional integral condition. The definition of the classical solution of the problem is given. 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. When solving the original inverse boundary value problem, the transition from the original inverse problem to some auxiliary inverse problem is carried out. The existence and uniqueness of a solution to an auxiliary problem are proved with the help of contracted mappings. Then the transition to the original inverse problem is again made, as a result, a conclusion is made about the solvability of the original inverse problem. [ABSTRACT FROM AUTHOR]

An inverse boundary-value problem for the pseudoparabolic equation of the third-order with integral condition is considered. First, the initial problem is reduced to an equivalent (in a certain meaning) problem, for which the theorem of existence and uniqueness is proved. Then, using these results, the existence and the uniqueness of the classical solution of the initial problem are proved. Keywords. Boundary-value problem, classical solution, Fourier method., Presented by A. E. Shishkov Introduction We know a lot of cases where the needs of practice lead to the problems of determination of coefficients or the right-hand side of [...]

In this paper, an inverse boundary value problem for a two‐dimensional hyperbolic equation with overdetermination conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence to the original problem in a certain sense. We then use the Fourier method to reduce such an equivalent problem to a system of integral equations. Furthermore, we prove the existence and uniqueness theorem for the auxiliary problem by the contraction mappings principle. Based on the equivalency of these problems, the existence and uniqueness theorem for the classical solution of the original inverse problem is proved. Some discussions on the numerical solutions for this inverse problem are presented including some numerical examples. [ABSTRACT FROM AUTHOR]

This article is concerned with the study of the unique solvability of a timenonlocal inverse boundary value problem for second-order hyperbolic equation with an integral overdetermination condition. To study the solvability of the inverse problem, we first reduce the considered problem to an auxiliary system with trivial data and prove its equivalence (in a certain sense) to the original problem. Then using the Banach fixed point principle, the existence and uniqueness of a solution to this system is shown. Further, on the basis of the equivalency of these problems the existence and uniqueness theorem for the classical solution of the inverse coefficient problem is proved for the smaller value of time. [ABSTRACT FROM AUTHOR]