scholarly journals A Numerical Method of Solving the Coefficient Inverse Problem for the Nonlinear Equation of Diffusion-Reaction

2018 ◽  
Vol 11 (1) ◽  
pp. 145-151
Author(s):  
Kh.M. Gamzaev ◽  
Keyword(s):  
Inverse Problem ◽  
Nonlinear Equation ◽  
Numerical Method ◽  
Diffusion Reaction ◽  
Coefficient Inverse Problem

scholarly journals A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

2018 ◽  
Vol 11 (4) ◽  
pp. 2339-2367 ◽  
Author(s):  
Michael V. Klibanov ◽  
Nikolay A. Koshev ◽  
Dinh-Liem Nguyen ◽  
Loc H. Nguyen ◽  
Aaron Brettin ◽  
...  
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Numerical Method ◽  
Coefficient Inverse Problem ◽  
Single Measurement

scholarly journals A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem

2020 ◽  
Vol 28 (3) ◽  
pp. 323-339 ◽  
Author(s):  
Phuong Mai Nguyen ◽  
Loc Hoang Nguyen
Keyword(s):  
Inverse Problem ◽  
Numerical Method ◽  
Parabolic Equations ◽  
Source Term ◽  
Nonlinear Coefficient ◽  
Time Variable ◽  
Inverse Source Problem ◽  
Coefficient Inverse Problem ◽  
Second Stage ◽  
Two Stages

AbstractTwo main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem to reconstruct a source term from external observations. Our method to solve this inverse source problem consists of two stages. We first establish an equation of the derivative of the solution to the parabolic equation with respect to the time variable. Then, in the second stage, we solve this equation by the quasi-reversibility method. The inverse source problem considered in this paper is the linearization of a nonlinear coefficient inverse problem. Hence, iteratively solving the inverse source problem provides the numerical solution to that coefficient inverse problem. Numerical results for the inverse source problem under consideration and the corresponding nonlinear coefficient inverse problem are presented.

scholarly journals A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data

2018 ◽  
Vol 12 (2) ◽  
pp. 493-523 ◽  
Author(s):  
Michael V. Klibanov ◽  
◽  
Dinh-Liem Nguyen ◽  
Loc H. Nguyen ◽  
Hui Liu ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Numerical Method ◽  
Frequency Data ◽  
Coefficient Inverse Problem ◽  
Single Measurement ◽  
Globally Convergent
Sign in / Sign up

Export Citation Format

Share Document