Eventual smoothness and stabilization of global weak solutions in parabolic–elliptic chemotaxis systems with logarithmic sensitivity
- Authors
- Ahn, Jaewook; Kang, Kyungkeun; Lee, Jihoon
- Issue Date
- Oct-2019
- Publisher
- Elsevier Ltd
- Keywords
- Chemotaxis; Eventual regularity; Large time behavior; Logarithmic sensitivity
- Citation
- Nonlinear Analysis: Real World Applications, v.49, pp 312 - 330
- Pages
- 19
- Journal Title
- Nonlinear Analysis: Real World Applications
- Volume
- 49
- Start Page
- 312
- End Page
- 330
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/18607
- DOI
- 10.1016/j.nonrwa.2019.03.012
- ISSN
- 1468-1218
- Abstract
- A parabolic–elliptic chemotaxis system with non-negative chemotactic sensitivity χ∕v and positive chemical diffusion coefficient η is considered in a smooth bounded domain Ω⊂R N , N≥2 under homogeneous Neumann boundary conditions. We show the existence of at least one global weak solution for χ<χ N , N≥3, where χ N ≔[Formula presented]. Moreover, under further assumptions of Ω and η, we prove that the constructed solution becomes smooth and stabilizes to a constant steady state after some waiting time if N=3,4. The stabilization of a global bounded solution, and the non-existence of non-constant steady states are also discussed in general dimensions. © 2019 Elsevier Ltd
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