English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The reaction-(cross-)diffusion system { ut = ∆(u φ(v)), x ∈ Ω, t > 0, vt = ∆v − v + u, x ∈ Ω, t > 0, (0.1) is considered under no-flux boundary conditions in smoothly bounded convex domains Ω ⊂ R, where m ≥ 1 and n ≥ 2, and where φ generalizes the prototype obtained on letting φ(v) = a+ b(v + d), v > 0, with a ≥ 0, b > 0, d ≥ 0 and α ≥ 0. In this framework, it is firstly seen that if m > n 2 , α < nm− 2 n− 2 and α < 2(m+ 1) n− 2 , then finite-time blow-up is excluded in the sense that for all suitably regular initial data an associated initial-boundary value problem admits a globally defined weak solution (u, v) with u being locally bounded in Ω× [0,∞). Under the assumption that additionally α < (n+ 2)m− n+ 2 2(n− 2) , these solutions are moreover shown to be bounded throughout Ω× (0,∞) in both components. In view of results known for the case m = 1, this particularly indicates that increasing m in (0.1) goes along with a certain regularizing effect despite the circumstance that thereby both the diffusion and the cross-diffusion mechanisms implicitly contained in (0.1) are simultaneously enhanced.

nonlinearity

Can simultaneous density-determined enhancement of diffusion and cross-diffusion foster boundedness in Keller–Segel type systems involving signal-dependent motilities?