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

^*Corresponding author for this work

Beijing Institute of Technology

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

Abstract

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.

Original language	English
Article number	109906
Journal	Applied Mathematics Letters
Volume	177
DOIs	https://doi.org/10.1016/j.aml.2026.109906
Publication status	Published - Jun 2026
Externally published	Yes

Keywords

Doubly degenerate diffusion
L-bounds
Nutrient taxis

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10.1016/j.aml.2026.109906

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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",

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

language = "English",

volume = "177",

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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

UR - https://www.scopus.com/pages/publications/105031095572

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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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Keywords

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