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Abstract and Applied Analysis
Volume 2014, Article ID 598135, 6 pages
Research Article

Conditional Stability for an Inverse Problem of Determining a Space-Dependent Source Coefficient in the Advection-Dispersion Equation with Robin’s Boundary Condition

1College of Mathematics and Statistics, Nanyang Normal University, Nanyang, Henan 473061, China
2Institute of Applied Mathematics, Shandong University of Technology, Zibo, Shandong 255049, China

Received 3 December 2013; Revised 27 February 2014; Accepted 27 February 2014; Published 24 April 2014

Academic Editor: Sergei V. Pereverzyev

Copyright © 2014 Shunqin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with an inverse problem of determining the space-dependent source coefficient in one-dimensional advection-dispersion equation with Robin’s boundary condition. Data compatibility for the inverse problem is analyzed by which an admissible set for the unknown is set forth. Furthermore, with the help of an integral identity, a conditional Lipschitz stability is established by suitably controlling the solution of an adjoint problem.