On Nonlinear Nonlocal Systems of Reaction Diffusion Equations
The reaction diffusion system with anomalous diffusion and a balance law ut+-Δα/2u=-fu,v, vt+-∆β/2v=fu,v, 0<α, β<2, is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction term f when 0<α≤β≤2; (ii) no grow...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/804784 |
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| _version_ | 1849404899289202688 |
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| author | B. Ahmad M. S. Alhothuali H. H. Alsulami M. Kirane S. Timoshin |
| author_facet | B. Ahmad M. S. Alhothuali H. H. Alsulami M. Kirane S. Timoshin |
| author_sort | B. Ahmad |
| collection | DOAJ |
| description | The reaction diffusion system with anomalous diffusion and a balance law ut+-Δα/2u=-fu,v, vt+-∆β/2v=fu,v, 0<α, β<2, is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction term f when 0<α≤β≤2; (ii) no growth condition is imposed on the reaction term f when 0<β≤α≤2. |
| format | Article |
| id | doaj-art-49623955321f46b4ba8cfc83f6fd634c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-49623955321f46b4ba8cfc83f6fd634c2025-08-20T03:36:48ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/804784804784On Nonlinear Nonlocal Systems of Reaction Diffusion EquationsB. Ahmad0M. S. Alhothuali1H. H. Alsulami2M. Kirane3S. Timoshin4Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaLaboratoire de Mathématiques, Images et Applications, Pôle Sciences et Technologies, Université de La Rochelle, Avenue M. Crepeau, 17031 La Rochelle, FranceDepartment of Mathematics, University College London, Gower Street, London WC1E 6BT, UKThe reaction diffusion system with anomalous diffusion and a balance law ut+-Δα/2u=-fu,v, vt+-∆β/2v=fu,v, 0<α, β<2, is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction term f when 0<α≤β≤2; (ii) no growth condition is imposed on the reaction term f when 0<β≤α≤2.http://dx.doi.org/10.1155/2014/804784 |
| spellingShingle | B. Ahmad M. S. Alhothuali H. H. Alsulami M. Kirane S. Timoshin On Nonlinear Nonlocal Systems of Reaction Diffusion Equations Abstract and Applied Analysis |
| title | On Nonlinear Nonlocal Systems of Reaction Diffusion Equations |
| title_full | On Nonlinear Nonlocal Systems of Reaction Diffusion Equations |
| title_fullStr | On Nonlinear Nonlocal Systems of Reaction Diffusion Equations |
| title_full_unstemmed | On Nonlinear Nonlocal Systems of Reaction Diffusion Equations |
| title_short | On Nonlinear Nonlocal Systems of Reaction Diffusion Equations |
| title_sort | on nonlinear nonlocal systems of reaction diffusion equations |
| url | http://dx.doi.org/10.1155/2014/804784 |
| work_keys_str_mv | AT bahmad onnonlinearnonlocalsystemsofreactiondiffusionequations AT msalhothuali onnonlinearnonlocalsystemsofreactiondiffusionequations AT hhalsulami onnonlinearnonlocalsystemsofreactiondiffusionequations AT mkirane onnonlinearnonlocalsystemsofreactiondiffusionequations AT stimoshin onnonlinearnonlocalsystemsofreactiondiffusionequations |