STABILIZATION FOR SMALL MASS IN A QUASILINEAR PARABOLIC–ELLIPTIC–ELLIPTIC ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH DENSITY-DEPENDENT SENSITIVITY: BALANCED CASE
STABILIZATION FOR SMALL MASS IN A QUASILINEAR PARABOLIC–ELLIPTIC–ELLIPTIC ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH DENSITY-DEPENDENT SENSITIVITY: BALANCED CASE
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发表时间：
2022
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通讯作者：
Y. Yokota
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作者：
Y. Yokota
研究了拟线性抛物-椭圆-椭圆吸引-排斥趋化系统的Neumann初边值问题，其中q = p，χα − <$γ = 0：在有界区域<$$> Rn（n ∈ N）中，边界光滑，其中m，p，q ∈ R，χ，<$，α，β，γ，δ > 0为常数.在m <$= 1，p <$= 2和q <$= 2的情况下，有界性和有限时间爆破已经通过p，q的大小和χα − <$γ（Z. Angew.数学物理; 2022; 73; 61），其中排除了临界情况χα − γ = 0。本文的目的是证明在χα − ε γ = 0的情况下的有界性和稳定性。
This paper is concerned with the Neumann initial-boundary problem for the quasilinear parabolic–elliptic–elliptic attraction-repulsion chemotaxis system with q = p and χα − ξγ = 0: in a bounded domain Ω ⊂ R n ( n ∈ N ) with smooth boundary ∂ Ω , where m , p , q ∈ R , χ , ξ , α , β , γ , δ > 0 are constants. In the case that m ̸ = 1, p ̸ = 2 and q ̸ = 2 boundedness and finite-time blow-up have been classified by the sizes of p , q and the sign of χα − ξγ (Z. Angew. Math. Phys.; 2022; 73; 61), where the critical case χα − ξγ = 0 has been excluded. The purpose of this paper is to prove boundedness and stabilization in the case χα − ξγ = 0.