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...
| Published in: | Advances in Nonlinear Analysis |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2024-10-01
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| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2024-0041 |
| _version_ | 1849754651592753152 |
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| author | Li Bin |
| author_facet | Li Bin |
| author_sort | Li Bin |
| collection | DOAJ |
| container_title | Advances in Nonlinear Analysis |
| description | 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. |
| format | Article |
| id | doaj-art-eabcf4e01d434a3f9a4dff83d1bfcfad |
| institution | Directory of Open Access Journals |
| issn | 2191-950X |
| language | English |
| publishDate | 2024-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| spelling | doaj-art-eabcf4e01d434a3f9a4dff83d1bfcfad2025-08-20T01:36:53ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2024-10-0113118520610.1515/anona-2024-0041Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networksLi Bin0School of Science, Ningbo University of Technology, Ningbo 315211, P. R. ChinaThe 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.https://doi.org/10.1515/anona-2024-0041parabolic-elliptic systemglobal existenceboundednesssteady state35k5535a0135b3535b4035q92 |
| spellingShingle | Li Bin Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks parabolic-elliptic system global existence boundedness steady state 35k55 35a01 35b35 35b40 35q92 |
| title | Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks |
| title_full | Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks |
| title_fullStr | Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks |
| title_full_unstemmed | Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks |
| title_short | Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks |
| title_sort | boundedness and long time behavior in a parabolic elliptic system arising from biological transport networks |
| topic | parabolic-elliptic system global existence boundedness steady state 35k55 35a01 35b35 35b40 35q92 |
| url | https://doi.org/10.1515/anona-2024-0041 |
| work_keys_str_mv | AT libin boundednessandlongtimebehaviorinaparabolicellipticsystemarisingfrombiologicaltransportnetworks |