A Revised Tikhonov Regularization Method for a Cauchy Problem of Two-Dimensional Heat Conduction Equation

Abstract

In this paper we investigate a Cauchy problem of two-dimensional (2D) heat conduction equation, which determines the internal surface temperature distribution from measured data at the fixed location. In general, this problem is ill-posed in the sense of Hadamard. We propose a revised Tikhonov regularization method to deal with this ill-posed problem and obtain the convergence estimate between the approximate solution and the exact one by choosing a suitable regularization parameter. A numerical example shows that the proposed method works well.

Regularization Error Analysis for a Sideways Problem of the 2D Nonhomogeneous Time-Fractional Diffusion Equation

“…Compared to the 1D setting, the literature of fractional diffusion equation in 2D or higher dimensional setting is much more scarce. Some articles [25][26][27][28] study the following 2D homogeneous fractional diffusion equation:…”

Identical approximation operator and regularization method for the Cauchy problem of 2‐D heat conduction equation

“…Previous studies [12][13][14] used Fourier method, simplified Tikhonov regularization method, and modified kernel method, respectively, to solve problem (1). Liu and Feng 15 utilized a revised Tikhonov regularization method for a Cauchy problem of 2-D heat conduction equation.…”