A free boundary problem for an attraction–repulsion chemotaxis system
Abstract In this paper we study an attraction–repulsion chemotaxis system with a free boundary in one space dimension. First, under some conditions, we investigate existence, uniqueness and uniform estimates of the global solution. Next, we prove a spreading–vanishing dichotomy for this model. In th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-12-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-018-1105-9 |
| _version_ | 1818443496585953280 |
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| author | Weiyi Zhang Zuhan Liu Ling Zhou |
| author_facet | Weiyi Zhang Zuhan Liu Ling Zhou |
| author_sort | Weiyi Zhang |
| collection | DOAJ |
| description | Abstract In this paper we study an attraction–repulsion chemotaxis system with a free boundary in one space dimension. First, under some conditions, we investigate existence, uniqueness and uniform estimates of the global solution. Next, we prove a spreading–vanishing dichotomy for this model. In the vanishing case, the species fail to establish and die out in the long run. In the spreading case, we provide some sufficient conditions to prove that the species successfully spread to infinity as t→∞ $t\rightarrow\infty$ and stabilize at a constant equilibrium state. The criteria for spreading and vanishing are also obtained. |
| first_indexed | 2024-12-14T19:00:58Z |
| format | Article |
| id | doaj.art-d36443f980b14bef9d19c2cc2c955c52 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-14T19:00:58Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-d36443f980b14bef9d19c2cc2c955c522022-12-21T22:50:57ZengSpringerOpenBoundary Value Problems1687-27702018-12-012018113810.1186/s13661-018-1105-9A free boundary problem for an attraction–repulsion chemotaxis systemWeiyi Zhang0Zuhan Liu1Ling Zhou2School of Mathematical Science, Yangzhou UniversitySchool of Mathematical Science, Yangzhou UniversitySchool of Mathematical Science, Yangzhou UniversityAbstract In this paper we study an attraction–repulsion chemotaxis system with a free boundary in one space dimension. First, under some conditions, we investigate existence, uniqueness and uniform estimates of the global solution. Next, we prove a spreading–vanishing dichotomy for this model. In the vanishing case, the species fail to establish and die out in the long run. In the spreading case, we provide some sufficient conditions to prove that the species successfully spread to infinity as t→∞ $t\rightarrow\infty$ and stabilize at a constant equilibrium state. The criteria for spreading and vanishing are also obtained.http://link.springer.com/article/10.1186/s13661-018-1105-9Attraction–repulsion chemotaxis systemFree boundarySpreading and vanishing |
| spellingShingle | Weiyi Zhang Zuhan Liu Ling Zhou A free boundary problem for an attraction–repulsion chemotaxis system Boundary Value Problems Attraction–repulsion chemotaxis system Free boundary Spreading and vanishing |
| title | A free boundary problem for an attraction–repulsion chemotaxis system |
| title_full | A free boundary problem for an attraction–repulsion chemotaxis system |
| title_fullStr | A free boundary problem for an attraction–repulsion chemotaxis system |
| title_full_unstemmed | A free boundary problem for an attraction–repulsion chemotaxis system |
| title_short | A free boundary problem for an attraction–repulsion chemotaxis system |
| title_sort | free boundary problem for an attraction repulsion chemotaxis system |
| topic | Attraction–repulsion chemotaxis system Free boundary Spreading and vanishing |
| url | http://link.springer.com/article/10.1186/s13661-018-1105-9 |
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