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On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity
Citation
Tello del Castillo, José Ignacio and Negreanu, Mihaela (2013). On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity. "Nonlinear Analysis: Theory, Methods & Applications", v. 80 (n. null); pp. 1-13. ISSN 0362-546X. https://doi.org/10.1016/j.na.2012.12.004.
Description
| Title: | On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity |
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| Author/s: |
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| Item Type: | Article |
| Título de Revista/Publicación: | Nonlinear Analysis: Theory, Methods & Applications |
| Date: | March 2013 |
| ISSN: | 0362-546X |
| Volume: | 80 |
| Subjects: | |
| Freetext Keywords: | Chemotaxis; Asymptotic behavior; Stability of solutions |
| Faculty: | E.U. de Informática (UPM) |
| Department: | Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones |
| Creative Commons Licenses: | Recognition - No derivative works - Non commercial |
Abstract
We study a parabolic–elliptic chemotactic system describing the evolution of a population’s density “u” and a chemoattractant’s concentration “v”. The system considers a non-constant chemotactic sensitivity given by “χ(N−u)”, for N≥0, and a source term of logistic type “λu(1−u)”. The existence of global bounded classical solutions is proved for any χ>0, N≥0 and λ≥0. By using a comparison argument we analyze the stability of the constant steady state u=1, v=1, for a range of parameters. – For N>1 and Nλ>2χ, any positive and bounded solution converges to the steady state. – For N≤1 the steady state is locally asymptotically stable and for χN<λ, the steady state is globally asymptotically stable.
More information
| Item ID: | 33253 |
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| DC Identifier: | http://oa.upm.es/33253/ |
| OAI Identifier: | oai:oa.upm.es:33253 |
| DOI: | 10.1016/j.na.2012.12.004 |
| Official URL: | http://www.sciencedirect.com/science/article/pii/S0362546X12004567 |
| Deposited by: | Memoria Investigacion |
| Deposited on: | 24 Apr 2015 18:42 |
| Last Modified: | 24 Apr 2015 18:42 |
