An inverse boundary value problem for a two-dimensional pseudo-parabolic equation of third order

Abstract

In the present work, we consider an inverse boundary value problem for a two-dimensional pseudo-parabolic equation of the third-order. Using analytical and operator-theoretic methods, as well as the Fourier method, the existence and uniqueness of the classical solution of this problem is proved. This inverse problem is formulated as an auxiliary inverse problem which, in turn, is reduced to the operator equation in a specified Banach space using the method of spectral analysis. In addition, the two-dimensional pseudo-parabolic problem is discretized using the FDM and reshaped as nonlinear least-squares optimization of the Tikhonov regularization function. This is numerically solved by means of the MATLAB subroutine lsqnonlin tool. Both analytical and perturbed data are inverted. Numerical outcomes for benchmark test example is reported and discussed.

Keywords

• Inverse boundary value problem
• Two-dimensional pseudo-parabolic equations of the third order
• Fourier method
• Riesz basis
• Contraction operator
• Tikhonov regularization