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Applied Mathematics-A Journal of Chinese Universities  2020, Vol. 35 Issue (2): 244-252    DOI: 10.1007/s11766-020-3994-5
    
Boundedness in a fully parabolic quasilinear repulsion chemotaxis model of higher dimension
ZHOU Shuang-shuang , GONG Ting, YANG Jin-ge
1School of Science, Hunan City University, Yiyang 413000, China.
2School of Mathematics, Dongbei University of Finance and Economics, Dalian 116024, China.
3School of Sciences, Nanchang Institute of Technology, Nanchang 330099, China.
Boundedness in a fully parabolic quasilinear repulsion chemotaxis model of higher dimension
ZHOU Shuang-shuang , GONG Ting, YANG Jin-ge
1School of Science, Hunan City University, Yiyang 413000, China.
2School of Mathematics, Dongbei University of Finance and Economics, Dalian 116024, China.
3School of Sciences, Nanchang Institute of Technology, Nanchang 330099, China.
 全文: PDF 
摘要： We deal with the boundedness of solutions to a class of fully parabolic quasilinear
repulsion chemotaxis systems
{
ut = ? · (?(u)?u) + ? · (ψ(u)?v), (x, t) ∈ ? × (0, T),
vt = ?v ? v + u, (x, t) ∈ ? × (0, T),
under homogeneous Neumann boundary conditions in a smooth bounded domain ? ? R
N (N ≥3), where 0 < ψ(u) ≤ K(u + 1)α, K1(s + 1)m ≤ ?(s) ≤ K2(s + 1)m with α, K, K1, K2 > 0 and
m ∈ R. It is shown that if α ? m < 4N+2 , then for any sufficiently smooth initial data, the
classical solutions to the system are uniformly-in-time bounded. This extends the known result
for the corresponding model with linear diffusion.
关键词： chemotaxis;  repulsion;  quasilinear;  fully parabolic;  boundedness;  high dimension    
Abstract: We deal with the boundedness of solutions to a class of fully parabolic quasilinear
repulsion chemotaxis systems
{
ut = ? · (?(u)?u) + ? · (ψ(u)?v), (x, t) ∈ ? × (0, T),
vt = ?v ? v + u, (x, t) ∈ ? × (0, T),
under homogeneous Neumann boundary conditions in a smooth bounded domain ? ? R
N (N ≥3), where 0 < ψ(u) ≤ K(u + 1)α, K1(s + 1)m ≤ ?(s) ≤ K2(s + 1)m with α, K, K1, K2 > 0 and
m ∈ R. It is shown that if α ? m < 4N+2 , then for any sufficiently smooth initial data, the
classical solutions to the system are uniformly-in-time bounded. This extends the known result
for the corresponding model with linear diffusion.
Key words: chemotaxis    repulsion    quasilinear    fully parabolic    boundedness    high dimension
出版日期: 2020-07-06
CLC:  35A01  
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ZHOU Shuang-shuang
GONG Ting
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引用本文:

ZHOU Shuang-shuang , GONG Ting, YANG Jin-ge. Boundedness in a fully parabolic quasilinear repulsion chemotaxis model of higher dimension[J]. Applied Mathematics-A Journal of Chinese Universities, 2020, 35(2): 244-252.

ZHOU Shuang-shuang , GONG Ting, YANG Jin-ge. Boundedness in a fully parabolic quasilinear repulsion chemotaxis model of higher dimension. Applied Mathematics-A Journal of Chinese Universities, 2020, 35(2): 244-252.

链接本文:

http://www.zjujournals.com/amjcub/CN/10.1007/s11766-020-3994-5    或    http://www.zjujournals.com/amjcub/CN/Y2020/V35/I2/244

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