Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks

The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-elliptic system arising from biological transport networks. For such problem, we first establish the global existence, uniqueness, and uniform boundedness of the strong solution by estimating the derivative o...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 13; no. 1; pp. 185 - 206
Main Author Li, Bin
Format Journal Article
LanguageEnglish
Published De Gruyter 08.10.2024
Subjects
35A01
35B35
35B40
35K55
35Q92
boundedness
global existence
parabolic-elliptic system
steady state
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Summary:The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-elliptic system arising from biological transport networks. For such problem, we first establish the global existence, uniqueness, and uniform boundedness of the strong solution by estimating the derivative of the diagonal permeability tensor with respect to time variable. Moreover, for the diffusion coefficient appropriately large, we demonstrate that the corresponding stationary problem admits a strong solution and that the solution of the Cauchy problem will stabilize to its stationary counterpart in infinite time with a time-decay rate.
ISSN:2191-950X
2191-950X
DOI:10.1515/anona-2024-0041