Global solvability for an indirect consumption chemotaxis system with signal-dependent motility

Ai Huang; Yifu Wang

doi:10.1016/j.aml.2024.109035

Global solvability for an indirect consumption chemotaxis system with signal-dependent motility

Ai Huang^*
, Yifu Wang

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

This paper considers the indirect signal consumption-chemotaxis system with signal-dependent motility in a smooth bounded domain Ω⊂Rⁿ(n≤3), as given by u_t=Δ(ϕ(v)u),v_t=Δv−vw,w_t=dΔw−w+u, where the motility function ϕ∈C³((0,∞)),ϕ>0 on (0,∞), which generalizes ϕ(v)=v^α,α∈R. Based on point-wise positive lower bound estimate of v, it is shown that for any suitably regular initial data, the corresponding initial–boundary value problem admits global smooth solutions.

Original language	English
Article number	109035
Journal	Applied Mathematics Letters
Volume	152
DOIs	https://doi.org/10.1016/j.aml.2024.109035
Publication status	Published - Jun 2024

Keywords

Chemotaxis
Degenerate diffusion
Global solvability
Singular diffusion

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10.1016/j.aml.2024.109035

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title = "Global solvability for an indirect consumption chemotaxis system with signal-dependent motility",

abstract = "This paper considers the indirect signal consumption-chemotaxis system with signal-dependent motility in a smooth bounded domain Ω⊂Rn(n≤3), as given by ut=Δ(ϕ(v)u),vt=Δv−vw,wt=dΔw−w+u, where the motility function ϕ∈C3((0,∞)),ϕ>0 on (0,∞), which generalizes ϕ(v)=vα,α∈R. Based on point-wise positive lower bound estimate of v, it is shown that for any suitably regular initial data, the corresponding initial{\textendash}boundary value problem admits global smooth solutions.",

keywords = "Chemotaxis, Degenerate diffusion, Global solvability, Singular diffusion",

author = "Ai Huang and Yifu Wang",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Ltd",

year = "2024",

month = jun,

doi = "10.1016/j.aml.2024.109035",

language = "English",

volume = "152",

journal = "Applied Mathematics Letters",

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T1 - Global solvability for an indirect consumption chemotaxis system with signal-dependent motility

AU - Huang, Ai

AU - Wang, Yifu

PY - 2024/6

Y1 - 2024/6

N2 - This paper considers the indirect signal consumption-chemotaxis system with signal-dependent motility in a smooth bounded domain Ω⊂Rn(n≤3), as given by ut=Δ(ϕ(v)u),vt=Δv−vw,wt=dΔw−w+u, where the motility function ϕ∈C3((0,∞)),ϕ>0 on (0,∞), which generalizes ϕ(v)=vα,α∈R. Based on point-wise positive lower bound estimate of v, it is shown that for any suitably regular initial data, the corresponding initial–boundary value problem admits global smooth solutions.

AB - This paper considers the indirect signal consumption-chemotaxis system with signal-dependent motility in a smooth bounded domain Ω⊂Rn(n≤3), as given by ut=Δ(ϕ(v)u),vt=Δv−vw,wt=dΔw−w+u, where the motility function ϕ∈C3((0,∞)),ϕ>0 on (0,∞), which generalizes ϕ(v)=vα,α∈R. Based on point-wise positive lower bound estimate of v, it is shown that for any suitably regular initial data, the corresponding initial–boundary value problem admits global smooth solutions.

KW - Chemotaxis

KW - Degenerate diffusion

KW - Global solvability

KW - Singular diffusion

UR - https://www.scopus.com/pages/publications/85185832567

U2 - 10.1016/j.aml.2024.109035

DO - 10.1016/j.aml.2024.109035

M3 - Article

AN - SCOPUS:85185832567

SN - 0893-9659

VL - 152

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 109035

ER -

Global solvability for an indirect consumption chemotaxis system with signal-dependent motility

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Keywords

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