Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source

Xiangdong Zhao

Czechoslovak Mathematical Journal (2024)

  • Issue: 1, page 127-151
  • ISSN: 0011-4642

Abstract

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We study the chemotaxis system with singular sensitivity and logistic-type source: u t = Δ u - χ ∇ · ( u ∇ v / v ) + r u - μ u k , 0 = Δ v - v + u under the non-flux boundary conditions in a smooth bounded domain Ω ⊂ ℝ n , χ , r , μ > 0 , k > 1 and n ≥ 1 . It is shown with k ∈ ( 1 , 2 ) that the system possesses a global generalized solution for n ≥ 2 which is bounded when χ > 0 is suitably small related to r > 0 and the initial datum is properly small, and a global bounded classical solution for n = 1 .

How to cite

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Zhao, Xiangdong. "Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source." Czechoslovak Mathematical Journal (2024): 127-151. <http://eudml.org/doc/299233>.

@article{Zhao2024,
abstract = {We study the chemotaxis system with singular sensitivity and logistic-type source: $u_t=\Delta u-\chi \nabla \cdot (u \nabla v/ v) +ru-\mu u^k$, $0=\Delta v-v+u$ under the non-flux boundary conditions in a smooth bounded domain $\Omega \subset \mathbb \{R\}^n$, $\chi ,r,\mu >0$, $k>1$ and $n\ge 1$. It is shown with $k\in (1,2)$ that the system possesses a global generalized solution for $n\ge 2$ which is bounded when $\chi >0$ is suitably small related to $r>0$ and the initial datum is properly small, and a global bounded classical solution for $n=1$.},
author = {Zhao, Xiangdong},
journal = {Czechoslovak Mathematical Journal},
keywords = {chemotaxis; singular sensitivity; global solvability},
language = {eng},
number = {1},
pages = {127-151},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source},
url = {http://eudml.org/doc/299233},
year = {2024},
}

TY - JOUR
AU - Zhao, Xiangdong
TI - Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 127
EP - 151
AB - We study the chemotaxis system with singular sensitivity and logistic-type source: $u_t=\Delta u-\chi \nabla \cdot (u \nabla v/ v) +ru-\mu u^k$, $0=\Delta v-v+u$ under the non-flux boundary conditions in a smooth bounded domain $\Omega \subset \mathbb {R}^n$, $\chi ,r,\mu >0$, $k>1$ and $n\ge 1$. It is shown with $k\in (1,2)$ that the system possesses a global generalized solution for $n\ge 2$ which is bounded when $\chi >0$ is suitably small related to $r>0$ and the initial datum is properly small, and a global bounded classical solution for $n=1$.
LA - eng
KW - chemotaxis; singular sensitivity; global solvability
UR - http://eudml.org/doc/299233
ER -

References

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