컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0143 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-08) Recent Trend in Fluid Equations (SS-08) |
| 발표시간(Time) | 20th-D-13:30 -- 13:50 |
| 영문제목 (Title(Eng.)) |
Thresholds for solution boundedness and blow-up in repulsive chemotaxis-consumption systems in higher dimensions |
| 저자(Author(s)) |
Jaewook Ahn1, Kyungkeun Kang2, Dongkwang Kim3 Dongguk University1, Yonsei University2, UNIST3 |
| 초록본문(Abstract) | We investigate repulsive chemotaxis-consumption systems described by \begin{align*} \partial_t u &= \nabla\cdot((1+u)^{m-1}\nabla u) + \nabla\cdot(u\nabla v),\\ 0&= \Delta v -uv \end{align*} in an $n$-dimensional ball, along with the no-flux/Dirichlet boundary conditions: \begin{equation*} \nu\cdot((1+u)^{m-1}\nabla u+u\nabla v)=0\,\text{ and }\, v=M. \end{equation*} Our analysis reveals a critical diffusive regime at $m=1$, establishing the conditions under which the system yields globally bounded solutions or leads to the blow-up of solutions. We first demonstrate that global-in-time bounded solutions exist for $m>1$, or for $m=1$ when $M$ is sufficiently small. Conversely, in the case of $0<m<1$ we prove that solution blow-up occurs for sufficiently large values of $M$, thereby establishing $m=1$ as a critical threshold. |
| 분류기호 (MSC number(s)) |
35B40, 35K65, 35Q92 |
| 키워드(Keyword(s)) | Chemotaxis, Keller-Segel, blow-up, global existence |
| 강연 형태 (Language of Session (Talk)) |
Korean |