Inverse problem for the prelinear filtration of ground water
Abstract
A parameter identification problem for nonlinear parabolic equation describing the prelinear filtration phenomenon is considered. It is shown that the problem admits a non-empty solution set which is stable with respect to perturbations in the cost functional and the data. The numerical method for solving the inverse problem is given and the computational results are presented.
References
[1] N.U. Ahmed. Optimization and Identification of Systems Governed by Evolution Equations on Banach Space. Pitman, Longman Scientific and Technical, 1988.
[2] H. Attouch. Variational Convergence for Functions and Operators. Pitman, London, 1984.
[3] C. Baiocchi and A. Capelo. Variational and Quasivariational Inequalities: Applications to Free Boundary Problems . Springer-Verlag, 1984.
[4] H.T. Banks, S. Reich, I.G . Rosen. Galerkin approximation of inverse problems for nonautonomous nonlinear distributed systems. Appl. Math. Optim. 24: 233- 256, 1991.
[5] V. Barbu. Analysis and Control of Nonlinear Infinite Dimensional Systems. Academic Press, Boston, 1993.
[2] H. Attouch. Variational Convergence for Functions and Operators. Pitman, London, 1984.
[3] C. Baiocchi and A. Capelo. Variational and Quasivariational Inequalities: Applications to Free Boundary Problems . Springer-Verlag, 1984.
[4] H.T. Banks, S. Reich, I.G . Rosen. Galerkin approximation of inverse problems for nonautonomous nonlinear distributed systems. Appl. Math. Optim. 24: 233- 256, 1991.
[5] V. Barbu. Analysis and Control of Nonlinear Infinite Dimensional Systems. Academic Press, Boston, 1993.
Published
2023-07-14
Issue
pp. 97-107
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Denkowski, Z., Migórski, S., Schaefer, R., & Telega, H. (2023). Inverse problem for the prelinear filtration of ground water. Computer Assisted Methods in Engineering and Science, 3(2), 97-107. https://cames3.ippt.pan.pl/index.php/cames/article/view/1448
