In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="&q...In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup>n</sup> (n ≥ 1), where d<sub>1</sub> > 0, d<sub>2</sub> > 0 with parameter χ ∈ R. When d<sub>1</sub> = d<sub>2</sub> + χ, satisfying for all initial data 0 ≤ n<sub>0</sub> ∈ C<sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < v<sub>0</sub>∈ W<sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞).展开更多
文摘In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup>n</sup> (n ≥ 1), where d<sub>1</sub> > 0, d<sub>2</sub> > 0 with parameter χ ∈ R. When d<sub>1</sub> = d<sub>2</sub> + χ, satisfying for all initial data 0 ≤ n<sub>0</sub> ∈ C<sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < v<sub>0</sub>∈ W<sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞).
