TY - JOUR
T1 - A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system
AU - Ahn, Jaewook
AU - Winkler, Michael
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2023/7
Y1 - 2023/7
N2 - The repulsive chemotaxis-consumption system {ut=∇·(D(u)∇u)+∇·(u∇v),0=Δv-uv, is considered along with the boundary conditions (D(u) ∇ u+ u∇ v) · ν| ∂Ω= 0 and v| ∂Ω= M in a ball Ω ⊂ R2 . Under the assumption that D suitably generalizes the function 0 ≤ ξ↦ (ξ+ 1) -α for some α> 0 , it is firstly shown that for each nontrivial radially symmetric u∈ W1,∞(Ω) , one can find M⋆(u) > 0 with the property that whenever M> M⋆(u) , a corresponding initial-boundary value problem admits a classical solution blowing up in finite time. This is complemented by a second statement which asserts that when inf D and M are positive, for any such initial data a global bounded classical solution exists.
AB - The repulsive chemotaxis-consumption system {ut=∇·(D(u)∇u)+∇·(u∇v),0=Δv-uv, is considered along with the boundary conditions (D(u) ∇ u+ u∇ v) · ν| ∂Ω= 0 and v| ∂Ω= M in a ball Ω ⊂ R2 . Under the assumption that D suitably generalizes the function 0 ≤ ξ↦ (ξ+ 1) -α for some α> 0 , it is firstly shown that for each nontrivial radially symmetric u∈ W1,∞(Ω) , one can find M⋆(u) > 0 with the property that whenever M> M⋆(u) , a corresponding initial-boundary value problem admits a classical solution blowing up in finite time. This is complemented by a second statement which asserts that when inf D and M are positive, for any such initial data a global bounded classical solution exists.
UR - http://www.scopus.com/inward/record.url?scp=85162956357&partnerID=8YFLogxK
U2 - 10.1007/s00526-023-02523-5
DO - 10.1007/s00526-023-02523-5
M3 - Article
AN - SCOPUS:85162956357
SN - 0944-2669
VL - 62
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 6
M1 - 180
ER -