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Existence and uniqueness of global weak solutions to degenerate volume-filling chemotaxis systems with source terms
Abstract
This paper is concerned with a no-flux initial-boundary value problem for the degenerate volume-filling chemotaxis system with source terms, ut = ∇ · (D(u,v) ∇ u − h(u,v) ∇ v) + f(x, u, v), vt = Δv + g(u,v), x∈ Ω, t>0 in a smoothly bounded domain Ω⊂ ℝN (N ∈ ℕ). It is shown that when D, h, f and g satisfy suitable assumptions involving D(1,·)=h(0,·)=h(1,·)=f(·,0,·) = f(·,1,·) = 0, for nonnegative initial data u0 and v0 with u0≤ 1, there exists a global weak solution $(u, v)$ with u≤ 1. In addition, uniqueness of global weak solutions is established when D(r,s) = D(r) for all r∈[0,1] and s∈[0,∞), and D, h, f, g and v0 are supposed to satisfy additional conditions.
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BibTeX
@misc{shibata2026existence,
title = {{Existence and uniqueness of global weak solutions to degenerate volume-filling chemotaxis systems with source terms}},
author = {Osuke Shibata},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29883},
eprint = {2609.29883},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29883},
}
RIS
TY - UNPB
TI - Existence and uniqueness of global weak solutions to degenerate volume-filling chemotaxis systems with source terms
AU - Osuke Shibata
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29883
UR - https://arxiv.org/abs/2609.29883
AB - This paper is concerned with a no-flux initial-boundary value problem for the degenerate volume-filling chemotaxis system with source terms, u_t = ∇ · (D(u,v) ∇ u − h(u,v) ∇ v) + f(x, u, v), v_t = Δv + g(u,v), x∈ Ω, t>0 in a smoothly bounded domain Ω⊂ ℝ^N (N ∈ ℕ). It is shown that when D, h, f and g satisfy suitable assumptions involving D(1,·)=h(0,·)=h(1,·)=f(·,0,·) = f(·,1,·) = 0, for nonnegative initial data u_0 and v_0 with u_0≤ 1, there exists a global weak solution $(u, v)$ with u≤ 1. In addition, uniqueness of global weak solutions is established when D(r,s) = D(r) for all r∈[0,1] and s∈[0,∞), and D, h, f, g and v_0 are supposed to satisfy additional conditions.
ER -