L∞ bounds in a three-dimensional doubly degenerate nutrient-taxis system

Xiang Mao De-Ji; Yifu Wang

doi:10.1016/j.aml.2026.109906

L∞ bounds in a three-dimensional doubly degenerate nutrient-taxis system

Xiang Mao De-Ji^*
, Yifu Wang

^*此作品的通讯作者

Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

This paper is concerned with the doubly degenerate nutrient taxis system u_t=∇⋅(uv∇u)−χ∇⋅(u^αv∇v)+ℓuv,v_t=Δv−uv, in a smoothly bounded domain Ω⊂R³ with parameters α>0, χ>0 and ℓ>0. It is shown that when α∈(32,1912), the corresponding global continuous weak solution to the zero-flux initial-boundary value problem remains uniformly bounded in time for reasonably regular initial data. The proof relies on the use of a novel class of functional inequality and a developed Moser-type iterative.

源语言	英语
期刊论文编号	109906
期刊	Applied Mathematics Letters
卷	177
DOI	https://doi.org/10.1016/j.aml.2026.109906
出版状态	已出版 - 6月 2026
已对外发布	是

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title = "L∞ bounds in a three-dimensional doubly degenerate nutrient-taxis system",

abstract = "This paper is concerned with the doubly degenerate nutrient taxis system ut=∇⋅(uv∇u)−χ∇⋅(uαv∇v)+ℓuv,vt=Δv−uv, in a smoothly bounded domain Ω⊂R3 with parameters α>0, χ>0 and ℓ>0. It is shown that when α∈(32,1912), the corresponding global continuous weak solution to the zero-flux initial-boundary value problem remains uniformly bounded in time for reasonably regular initial data. The proof relies on the use of a novel class of functional inequality and a developed Moser-type iterative.",

keywords = "Doubly degenerate diffusion, L-bounds, Nutrient taxis",

author = "De-Ji, \{Xiang Mao\} and Yifu Wang",

note = "Publisher Copyright: Copyright {\textcopyright} 2026. Published by Elsevier Ltd.",

year = "2026",

month = jun,

doi = "10.1016/j.aml.2026.109906",

language = "English",

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T1 - L∞ bounds in a three-dimensional doubly degenerate nutrient-taxis system

AU - De-Ji, Xiang Mao

AU - Wang, Yifu

PY - 2026/6

Y1 - 2026/6

N2 - This paper is concerned with the doubly degenerate nutrient taxis system ut=∇⋅(uv∇u)−χ∇⋅(uαv∇v)+ℓuv,vt=Δv−uv, in a smoothly bounded domain Ω⊂R3 with parameters α>0, χ>0 and ℓ>0. It is shown that when α∈(32,1912), the corresponding global continuous weak solution to the zero-flux initial-boundary value problem remains uniformly bounded in time for reasonably regular initial data. The proof relies on the use of a novel class of functional inequality and a developed Moser-type iterative.

AB - This paper is concerned with the doubly degenerate nutrient taxis system ut=∇⋅(uv∇u)−χ∇⋅(uαv∇v)+ℓuv,vt=Δv−uv, in a smoothly bounded domain Ω⊂R3 with parameters α>0, χ>0 and ℓ>0. It is shown that when α∈(32,1912), the corresponding global continuous weak solution to the zero-flux initial-boundary value problem remains uniformly bounded in time for reasonably regular initial data. The proof relies on the use of a novel class of functional inequality and a developed Moser-type iterative.

KW - Doubly degenerate diffusion

KW - L-bounds

KW - Nutrient taxis

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DO - 10.1016/j.aml.2026.109906

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VL - 177

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 109906

ER -

L∞ bounds in a three-dimensional doubly degenerate nutrient-taxis system

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