| Title | STOCHASTIC DYNAMIC MODEL FOR POROUS MEDIA EQUATION DESCRIBING UNDERGROUND RESOURCES |
| Publication Type | Journal Article |
| Year of Publication | 2009 |
| Authors | AHMED, NU, KERBAL, S |
| Secondary Title | Communications in Applied Analysis |
| Volume | 13 |
| Issue | 2 |
| Start Page | 271 |
| Pagination | 286 |
| Date Published | 04/2009 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 34A36, 34A60, 49J24, 93C10, 93E20 |
| Abstract | We consider a stochastic model for porous media flow. This is a degenerate nonlinear stochastic parabolic partial differential equation which may change type from parabolic to elliptic and vice versa. We present existence and regularity of weak solutions. We formulate certain control problems for aquifers (under ground water reservoirs) and discuss some open problems.
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| URL | http://www.acadsol.eu/en/articles/13/2/8.pdf |
| Short Title | STOCHASTIC DYNAMICS FOR AQUIFERS |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] N. U. Ahmed, Porous medium dynamics with optimal control and extraction of underground resources, Dynam. Continuous Discrete Impulsive Systems 15 (2008), 711–725.
[2] N. U. Ahmed, Dynamics of flow in porous media and its control applied to optimal management of underground resources, Comm. Appl. Anal. 122 (2008), 221–234. [3] A. V. Skorokhod, Studies in Theory of Randam Processes,Addison-Wesley Publishing Company, Inc. Massachusetts, 1965. [4] N. U. Ahmed and K. L. Teo, Optimal Control of Distributed Parameter Systems, Elsevier North Holland Inc. , New York, Oxford, 1981. [5] R. E. Showlter, Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 491997. [6] V. Barbu, G. Da Prato and M. Rockner, Some Results on Stochastic Porous Media Equations, www.physik.uni-bielefeld.de/bibos/preprints/08-04-283.pdf. [7] S. Willard, General Topology, Addison-Wesley Pub. Co., Massachusetts, Menlo Park, California, London, Don mils, Ontario, 1970. [8] N. U. Ahmed, Optimal choice of nonlinear output feedback control law for a class of uncertain parabolic systems,Dynamic Systems and Applications,17 (2008),571–582. |