2019/06/05 by Loc H. Nguyen, Nguyen, Loc Hoang · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1906.01931
openalex publication_date 2019/06/05 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28
We propose a robust numerical method to find the coefficient of the creation\nor depletion term of parabolic equations from the measurement of the lateral\nCauchy information of their solutions. Most papers in the field study this\nnonlinear and severely ill-posed problem using optimal control. The main\ndrawback of this widely used approach is the need of some advanced knowledge of\nthe true solution. In this paper, we propose a new method that opens a door to\nsolve nonlinear inverse problems for parabolic equations without any initial\nguess of the true coefficient. This claim is confirmed numerically. The key\npoint of the method is to derive a system of nonlinear elliptic equations for\nthe Fourier coefficients of the solution to the governing equation with respect\nto a special basis of L2. We then solve this system by a predictor-corrector\nprocess, in which our computation to obtain the first and second predictors is\neffective. The desired solution to the inverse problem under consideration\nfollows.\n