Blow-up and delay for a parabolic–elliptic Keller–Segel system with a source term
Abstract In this paper, we are concerned with the parabolic–elliptic Keller–Segel system with a positive source term in a bounded domain in RN ${\mathbb{R}}^{N}$ ( N=2,3 $N=2,3$), under homogeneous Dirichlet boundary condition, with time-dependent coefficients. Lower bounds for the blow-up time if t...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-06-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-018-1013-z |
| _version_ | 1811281769015541760 |
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| author | Yujuan Jiao Wenjing Zeng |
| author_facet | Yujuan Jiao Wenjing Zeng |
| author_sort | Yujuan Jiao |
| collection | DOAJ |
| description | Abstract In this paper, we are concerned with the parabolic–elliptic Keller–Segel system with a positive source term in a bounded domain in RN ${\mathbb{R}}^{N}$ ( N=2,3 $N=2,3$), under homogeneous Dirichlet boundary condition, with time-dependent coefficients. Lower bounds for the blow-up time if the solutions blow up in finite time are derived under appropriate assumptions on data. Moreover, the exponential decay of the associated energies is also studied. |
| first_indexed | 2024-04-13T01:39:35Z |
| format | Article |
| id | doaj.art-5c9c6790788243d1ac609975bfcd9c4d |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-13T01:39:35Z |
| publishDate | 2018-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-5c9c6790788243d1ac609975bfcd9c4d2022-12-22T03:08:14ZengSpringerOpenBoundary Value Problems1687-27702018-06-012018111010.1186/s13661-018-1013-zBlow-up and delay for a parabolic–elliptic Keller–Segel system with a source termYujuan Jiao0Wenjing Zeng1College of Mathematics and Computer Science, Northwest Minzu UniversityCollege of Mathematics and Computer Science, Northwest Minzu UniversityAbstract In this paper, we are concerned with the parabolic–elliptic Keller–Segel system with a positive source term in a bounded domain in RN ${\mathbb{R}}^{N}$ ( N=2,3 $N=2,3$), under homogeneous Dirichlet boundary condition, with time-dependent coefficients. Lower bounds for the blow-up time if the solutions blow up in finite time are derived under appropriate assumptions on data. Moreover, the exponential decay of the associated energies is also studied.http://link.springer.com/article/10.1186/s13661-018-1013-zParabolic–elliptic Keller–Segel systemBlow-up timeLower boundsDecay |
| spellingShingle | Yujuan Jiao Wenjing Zeng Blow-up and delay for a parabolic–elliptic Keller–Segel system with a source term Boundary Value Problems Parabolic–elliptic Keller–Segel system Blow-up time Lower bounds Decay |
| title | Blow-up and delay for a parabolic–elliptic Keller–Segel system with a source term |
| title_full | Blow-up and delay for a parabolic–elliptic Keller–Segel system with a source term |
| title_fullStr | Blow-up and delay for a parabolic–elliptic Keller–Segel system with a source term |
| title_full_unstemmed | Blow-up and delay for a parabolic–elliptic Keller–Segel system with a source term |
| title_short | Blow-up and delay for a parabolic–elliptic Keller–Segel system with a source term |
| title_sort | blow up and delay for a parabolic elliptic keller segel system with a source term |
| topic | Parabolic–elliptic Keller–Segel system Blow-up time Lower bounds Decay |
| url | http://link.springer.com/article/10.1186/s13661-018-1013-z |
| work_keys_str_mv | AT yujuanjiao blowupanddelayforaparabolicelliptickellersegelsystemwithasourceterm AT wenjingzeng blowupanddelayforaparabolicelliptickellersegelsystemwithasourceterm |