A Weak Solution of a Stochastic Nonlinear Problem
We consider a problem modeling a porous medium with a random perturbation. This model occurs in many applications such as biology, medical sciences, oil exploitation, and chemical engineering. Many authors focused their study mostly on the deterministic case. The more classical one was due to Biot i...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/482410 |
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| _version_ | 1849307988503822336 |
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| author | M. L. Hadji |
| author_facet | M. L. Hadji |
| author_sort | M. L. Hadji |
| collection | DOAJ |
| description | We consider a problem modeling a porous medium with a random perturbation. This model occurs in many applications such as biology, medical sciences, oil exploitation, and chemical engineering. Many authors focused their study mostly on the deterministic case. The more classical one was due to Biot in the 50s, where he suggested to ignore everything that happens at the microscopic level, to apply the principles of the continuum mechanics at the macroscopic level. Here we consider a stochastic problem, that is, a problem with a random perturbation. First we prove a result on the existence and uniqueness of the solution, by making use of the weak formulation. Furthermore, we use a numerical scheme based on finite differences to present numerical results. |
| format | Article |
| id | doaj-art-1fa4efb831f34ceb866ea4e5283d26a4 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1fa4efb831f34ceb866ea4e5283d26a42025-08-20T03:54:34ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/482410482410A Weak Solution of a Stochastic Nonlinear ProblemM. L. Hadji0Laboratory of Probability and Statistics (LAPS), Badji Mokhtar University, P.O. Box 12, 23000 Annaba, AlgeriaWe consider a problem modeling a porous medium with a random perturbation. This model occurs in many applications such as biology, medical sciences, oil exploitation, and chemical engineering. Many authors focused their study mostly on the deterministic case. The more classical one was due to Biot in the 50s, where he suggested to ignore everything that happens at the microscopic level, to apply the principles of the continuum mechanics at the macroscopic level. Here we consider a stochastic problem, that is, a problem with a random perturbation. First we prove a result on the existence and uniqueness of the solution, by making use of the weak formulation. Furthermore, we use a numerical scheme based on finite differences to present numerical results.http://dx.doi.org/10.1155/2015/482410 |
| spellingShingle | M. L. Hadji A Weak Solution of a Stochastic Nonlinear Problem Abstract and Applied Analysis |
| title | A Weak Solution of a Stochastic Nonlinear Problem |
| title_full | A Weak Solution of a Stochastic Nonlinear Problem |
| title_fullStr | A Weak Solution of a Stochastic Nonlinear Problem |
| title_full_unstemmed | A Weak Solution of a Stochastic Nonlinear Problem |
| title_short | A Weak Solution of a Stochastic Nonlinear Problem |
| title_sort | weak solution of a stochastic nonlinear problem |
| url | http://dx.doi.org/10.1155/2015/482410 |
| work_keys_str_mv | AT mlhadji aweaksolutionofastochasticnonlinearproblem AT mlhadji weaksolutionofastochasticnonlinearproblem |