On a Class of Reaction-Diffusion Equations with Aggregation
In this paper, global-in-time existence and blow-up results are shown for a reaction-diffusion equation appearing in the theory of aggregation phenomena (including chemotaxis). Properties of the corresponding steady-state problem are also presented. Moreover, the stability around constant equilibria...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-02-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2020-2092 |
| _version_ | 1811185948108521472 |
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| author | Chen Li Desvillettes Laurent Latos Evangelos |
| author_facet | Chen Li Desvillettes Laurent Latos Evangelos |
| author_sort | Chen Li |
| collection | DOAJ |
| description | In this paper, global-in-time existence and blow-up results are shown for a reaction-diffusion equation appearing in the theory of aggregation phenomena (including chemotaxis). Properties of the corresponding steady-state problem are also presented. Moreover, the stability around constant equilibria and the non-existence of nonconstant solutions are studied in certain cases. |
| first_indexed | 2024-04-11T13:37:59Z |
| format | Article |
| id | doaj.art-c98d1de79411409db71d4bb4a9b3f83a |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-11T13:37:59Z |
| publishDate | 2021-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-c98d1de79411409db71d4bb4a9b3f83a2022-12-22T04:21:24ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752021-02-0121111913310.1515/ans-2020-2092On a Class of Reaction-Diffusion Equations with AggregationChen Li0Desvillettes Laurent1Latos Evangelos2Universität Mannheim, 68131Mannheim, GermanyUniversité Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, F-75013, Paris, FranceUniversity of Graz, Institute for Mathematics and Scientific Computing, Heinrichstr. 36, A-8010Graz, AustriaIn this paper, global-in-time existence and blow-up results are shown for a reaction-diffusion equation appearing in the theory of aggregation phenomena (including chemotaxis). Properties of the corresponding steady-state problem are also presented. Moreover, the stability around constant equilibria and the non-existence of nonconstant solutions are studied in certain cases.https://doi.org/10.1515/ans-2020-2092reaction-diffusion with aggregationglobal existence of classical solutionsblow-upstability35b44 35k57 35b09 35k10 |
| spellingShingle | Chen Li Desvillettes Laurent Latos Evangelos On a Class of Reaction-Diffusion Equations with Aggregation Advanced Nonlinear Studies reaction-diffusion with aggregation global existence of classical solutions blow-up stability 35b44 35k57 35b09 35k10 |
| title | On a Class of Reaction-Diffusion Equations with Aggregation |
| title_full | On a Class of Reaction-Diffusion Equations with Aggregation |
| title_fullStr | On a Class of Reaction-Diffusion Equations with Aggregation |
| title_full_unstemmed | On a Class of Reaction-Diffusion Equations with Aggregation |
| title_short | On a Class of Reaction-Diffusion Equations with Aggregation |
| title_sort | on a class of reaction diffusion equations with aggregation |
| topic | reaction-diffusion with aggregation global existence of classical solutions blow-up stability 35b44 35k57 35b09 35k10 |
| url | https://doi.org/10.1515/ans-2020-2092 |
| work_keys_str_mv | AT chenli onaclassofreactiondiffusionequationswithaggregation AT desvilletteslaurent onaclassofreactiondiffusionequationswithaggregation AT latosevangelos onaclassofreactiondiffusionequationswithaggregation |