Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source

verfasst von: Tobias Black, Mario Fuest, Johannes Lankeit, Masaaki Mizukami
Abstract: We discuss the influence of possible spatial inhomogeneities in the coefficients of logistic source terms in parabolic–elliptic chemotaxis-growth systems of the form u_t=Δu−∇⋅(u∇v)+κ(x)u−μ(x)u²,0=Δv−v+u in smoothly bounded domains Ω⊂R². Assuming that the coefficient functions satisfy κ,μ∈C⁰(Ω¯) with μ≥0 we prove that finite-time blow-up of the classical solution can only occur in points where μ is zero, i.e. that the blow-up set B is contained in {x∈Ω¯∣μ(x)=0}.Moreover, we show that whenever μ(x₀)>0 for some x₀∈Ω¯, then one can find an open neighbourhood U of x₀ in Ω¯ such that u remains bounded in U throughout evolution.
Organisationseinheit(en): Institut für Angewandte Mathematik
Externe Organisation(en): Universität Paderborn
Kyoto University of Education
Typ: Artikel
Journal: Nonlinear Analysis: Real World Applications
Band: 73
ISSN: 1468-1218
Publikationsdatum: 10.2023
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Analysis, Allgemeiner Maschinenbau, Volkswirtschaftslehre, Ökonometrie und Finanzen (insg.), Computational Mathematics, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.48550/arXiv.2209.14184 (Zugang: Offen)
https://doi.org/10.1016/j.nonrwa.2023.103868 (Zugang: Geschlossen)