Identification of the source for full parabolic equations

• Main Author: Guillermo Federico Umbricht
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2021-07-01
• Series: Mathematical Modelling and Analysis
• Subjects: inverse and ill-posed problem; regularization operator; transport equation; fourier transform
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/12700

In this work, we consider the problem of identifying the time independent source for full parabolic equations in Rn from noisy data. This is an ill-posed problem in the sense of Hadamard. To compensate the factor that causes the instability, a family of parametric regularization operators is introduced, where the rule to select the value of the regularization parameter is included. This rule, known as regularization parameter choice rule, depends on the data noise level and the degree of smoothness that it is assumed for the source. The proof for the stability and convergence of the regularization criteria is presented and a Hölder type bound is obtained for the estimation error. Numerical examples are included to illustrate the effectiveness of this regularization approach.