Blow-up and delay for a parabolic–elliptic Keller–Segel system with a source term

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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Main Authors: Yujuan Jiao, Wenjing Zeng
Format: Article
Language:English
Published: SpringerOpen 2018-06-01
Series:Boundary Value Problems
Subjects:
Parabolic–elliptic Keller–Segel system
Blow-up time
Lower bounds
Decay
Online Access:http://link.springer.com/article/10.1186/s13661-018-1013-z
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spelling doaj-5c9c6790788243d1ac609975bfcd9c4d2020-11-25T00:21:33ZengSpringerOpenBoundary 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
collection DOAJ
language English
format Article
sources DOAJ
author Yujuan Jiao
Wenjing Zeng
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
author_facet Yujuan Jiao
Wenjing Zeng
author_sort Yujuan Jiao
title 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_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_sort blow-up and delay for a parabolic–elliptic keller–segel system with a source term
publisher SpringerOpen
series Boundary Value Problems
issn 1687-2770
publishDate 2018-06-01
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.
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
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