An inverse problem of determining the time-dependent potential in a higher-order Boussinesq-Love equation from boundary data

Abstract

PurposeThe paper aims to numerically solve the inverse problem of determining the time-dependent potential coefficient along with the temperature in a higher-order Boussinesq-Love equation (BLE) with initial and Neumann boundary conditions supplemented by boundary data, for the first time.Design/methodology/approachFrom the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, the authors apply the generalized finite difference method (GFDM) for solving the BLE along with the Tikhonov regularization to find stable and accurate numerical solutions. The regularized nonlinear minimization is performed using the MATLAB subroutine lsqnonlin. The stability analysis of solution of the BLE is proved using the von Neumann method.FindingsThe present numerical results demonstrate that obtained solutions are stable and accurate.Practical implicationsSince noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.Originality/valueThe knowledge of this physical property coefficient is very important in various areas of human activity such as seismology, mineral exploration, biology, medicine, quality control of industrial products, etc. The originality lies in the insight gained by performing the numerical simulations of inversion to find the potential co-efficient on time in the BLE from noisy measurement.

On Solvability of Some Inverse Problems for a Fractional Parabolic Equation with a Nonlocal Biharmonic Operator

“…As far as we know, the initial-boundary value problems for partial differential equations of fractional order with operators of the fourth and higher orders have been insufficiently studied. In this direction, we can note works [17][18][19][20][21][22][23][24] where, in particular, the inverse problems were also studied.…”

Identification of time‐dependent potential in a fourth‐order pseudo‐hyperbolic equation from additional measurement

“…Recently, the authors of previous studies [18][19][20] studied an inverse problem to reconstruct the time or space-dependent potential coefficients in the third-order pseudo-parabolic equation, while the authors of other research [21][22][23][24] continued to identify the time-dependent potential in the fourth-order Boussinesq-Love and pseudo-hyperbolic equations. Tekin 25 determined the time-dependent potential in a pseudo-hyperbolic problem theoretically with an overdetermination condition.…”

Reconstruction of a potential coefficient in the Rayleigh–Love equation with non-classical boundary condition

“…Furthermore, the investigation of the inverse problem for the fourth-order pseudo-hyperbolic equation with an over-determination condition is examined in Tekin (2019b), with nonlocal integral conditions in Huntul and Tamsir (2021b) and Megraliev and Alizade (2016), with additional conditions in Zamyshlyaeva et al. (2020), and with the additional temperature measurement in Huntul et al. (2021b).…”