Details
| Original language | English |
|---|---|
| Pages (from-to) | 4093-4109 |
| Number of pages | 17 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 26 |
| Issue number | 8 |
| Publication status | Published - Aug 2021 |
| Externally published | Yes |
Abstract
We construct global generalized solutions to the chemotaxis system (equation presented) in smooth, bounded domains Ω ⊂ Rn, n ≥2, for certain choices of λ; μ and κ. Here, inter alia, the selections μ(x) = jxjα with α < 2 and κ = 2 as well as μ ≡ μ1 > 0 and κ > minf 2n-2 n ; 2n+4 n+4 g are admissible (in both cases for any sufficiently smooth λ). While the former case appears to be novel in general, in the two- and threedimensional setting, the latter improves on a recent result by Winkler (Adv. Nonlinear Anal. 9 (2019), no. 1, 526-566), where the condition κ > 2n+4 n+4 has been imposed. In particular, for n = 2, our result shows that taking any κ > 1 suffices to exclude the possibility of collapse into a persistent Dirac distribution.
Keywords
- Chemotaxis, Generalized solutions, Heterogeneous environment, Logistic source
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Applied Mathematics
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In: Discrete and Continuous Dynamical Systems - Series B, Vol. 26, No. 8, 08.2021, p. 4093-4109.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - When do keller-segel systems with heterogeneous logistic sources admit generalized solutions?
AU - Yan, Jianlu
AU - Fuest, Mario
N1 - Publisher Copyright: © 2021 American Institute of Mathematical Sciences. All rights reserved.
PY - 2021/8
Y1 - 2021/8
N2 - We construct global generalized solutions to the chemotaxis system (equation presented) in smooth, bounded domains Ω ⊂ Rn, n ≥2, for certain choices of λ; μ and κ. Here, inter alia, the selections μ(x) = jxjα with α < 2 and κ = 2 as well as μ ≡ μ1 > 0 and κ > minf 2n-2 n ; 2n+4 n+4 g are admissible (in both cases for any sufficiently smooth λ). While the former case appears to be novel in general, in the two- and threedimensional setting, the latter improves on a recent result by Winkler (Adv. Nonlinear Anal. 9 (2019), no. 1, 526-566), where the condition κ > 2n+4 n+4 has been imposed. In particular, for n = 2, our result shows that taking any κ > 1 suffices to exclude the possibility of collapse into a persistent Dirac distribution.
AB - We construct global generalized solutions to the chemotaxis system (equation presented) in smooth, bounded domains Ω ⊂ Rn, n ≥2, for certain choices of λ; μ and κ. Here, inter alia, the selections μ(x) = jxjα with α < 2 and κ = 2 as well as μ ≡ μ1 > 0 and κ > minf 2n-2 n ; 2n+4 n+4 g are admissible (in both cases for any sufficiently smooth λ). While the former case appears to be novel in general, in the two- and threedimensional setting, the latter improves on a recent result by Winkler (Adv. Nonlinear Anal. 9 (2019), no. 1, 526-566), where the condition κ > 2n+4 n+4 has been imposed. In particular, for n = 2, our result shows that taking any κ > 1 suffices to exclude the possibility of collapse into a persistent Dirac distribution.
KW - Chemotaxis
KW - Generalized solutions
KW - Heterogeneous environment
KW - Logistic source
UR - http://www.scopus.com/inward/record.url?scp=85105973285&partnerID=8YFLogxK
U2 - 10.3934/dcdsb.2020275
DO - 10.3934/dcdsb.2020275
M3 - Article
AN - SCOPUS:85105973285
VL - 26
SP - 4093
EP - 4109
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 8
ER -