Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the probl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-07-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2020-0189 |
| _version_ | 1811280158200430592 |
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| author | Carrillo Antonio José Lin Ke |
| author_facet | Carrillo Antonio José Lin Ke |
| author_sort | Carrillo Antonio José |
| collection | DOAJ |
| description | We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the problem admits a global weak solution obtained by the limits of strong solutions to an approximated system. Based on the second moment of solutions, initial data are constructed to make sure blow up occurs in finite time on and below these curves (i.e. critical and supercritical cases). In addition, the existence or non-existence of minimizers of free energy functional is discussed on the critical curves and the solutions exist globally in time if the size of initial data is small. We also investigate the crossing point between the critical lines in which a refined criteria in terms of the masses is given again to distinguish the dichotomy between global existence and blow up. We also show that the blow ups is simultaneous for both species. |
| first_indexed | 2024-04-13T01:08:36Z |
| format | Article |
| id | doaj.art-22fe78b727ba4dbc96658e2bba5eee83 |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-04-13T01:08:36Z |
| publishDate | 2021-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-22fe78b727ba4dbc96658e2bba5eee832022-12-22T03:09:15ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2021-07-0111113910.1515/anona-2020-0189Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction systemCarrillo Antonio José0Lin Ke1Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UKSchool of Economics and Mathematics, Southwestern University of Economics and Finance, Chengdu, 611130, Sichuan ChinaWe consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the problem admits a global weak solution obtained by the limits of strong solutions to an approximated system. Based on the second moment of solutions, initial data are constructed to make sure blow up occurs in finite time on and below these curves (i.e. critical and supercritical cases). In addition, the existence or non-existence of minimizers of free energy functional is discussed on the critical curves and the solutions exist globally in time if the size of initial data is small. We also investigate the crossing point between the critical lines in which a refined criteria in terms of the masses is given again to distinguish the dichotomy between global existence and blow up. We also show that the blow ups is simultaneous for both species.https://doi.org/10.1515/anona-2020-0189degenerate parabolic systemchemotaxisvariational methodsglobal existenceblow up35k6592c1735j2035a0135b44 |
| spellingShingle | Carrillo Antonio José Lin Ke Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system Advances in Nonlinear Analysis degenerate parabolic system chemotaxis variational methods global existence blow up 35k65 92c17 35j20 35a01 35b44 |
| title | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_full | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_fullStr | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_full_unstemmed | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_short | Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system |
| title_sort | sharp conditions on global existence and blow up in a degenerate two species and cross attraction system |
| topic | degenerate parabolic system chemotaxis variational methods global existence blow up 35k65 92c17 35j20 35a01 35b44 |
| url | https://doi.org/10.1515/anona-2020-0189 |
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