Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model

• Published in: Bulletin of mathematical sciences Vol. 13; no. 2
• Main Author: Winkler, Michael
• Format: Journal Article
• Language: English
• Published: World Scientific Publishing Company 01.08.2023; World Scientific Publishing
• Subjects: a priori estimate; Chemotaxis; degenerate diffusion; Chemotaxis; degenerate diffusion; a priori estimate

A no-flux initial-boundary value problem for the cross-diffusion system u t = Δ ( u ϕ ( v ) ) , v t = Δ v − u v is considered in smoothly bounded domains Ω ⊂ ℝ n with n ≤ 2 . It is shown that whenever ϕ ∈ C 0 ( [ 0 , ∞ ) ) is positive on ( 0 , ∞ ) and such that lim inf ξ ↘ 0 ϕ ( ξ ) ξ α > 0 ( ⋆ )...