Abstract
It was shown that unbounded solutions of the Neumann initial-boundary value problem to the two-dimensional Keller-Segel system can be induced by initial data having large negative energy if the total mass Λ ∈ (4π, ∞) \ 4π · N and an example of such an initial datum was given for some transformed system and its associated energy in Horstmann-Wang (2001). In this work, we provide an alternative construction of nonnegative nonradially symmetric initial data enforcing unbounded solutions to the original Keller-Segel model.
Original language | English |
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Pages (from-to) | 1-12 |
Number of pages | 12 |
Journal | Mathematics In Engineering |
Volume | 4 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- Chemotaxis
- Infinite-time blow-up
- Keller-Segel system
- Local sensing
- Lyapunov functional
- Unbounded solution
ASJC Scopus subject areas
- Applied Mathematics
- Mathematical Physics
- Analysis