论文标题
具有竞争动力学和非本地术语的趋化性和渐近性稳定性
Boundedness and asymptotically stability to chemotaxis system with competitive kinetics and nonlocal terms
论文作者
论文摘要
本文介绍了使用竞争动力学和非局部术语\ begin {eqnarray*} \ left \ left \ {\ begin {array} {llll}u_1Δu-t =d_1Δu-χ_1\ nabla \ cdot（u \ nabla（u \ nabla） w）+u \ left（a_0-a_1u-a_ {2} v-a_3 \int_Ω w）+v \ left（b_0-b_1u-b_ {2} v-b_3 \int_Ω \ end {eqnarray*}在平稳界限的域中$ω\ subset \ mathbb {r}^n，n \ geq1 $，其中$ a_0，a_0，a_1，a_1，a_2，b_0，b_1，b_1，b_2> 0 $ a_4，a_4，a_4，a_4，a_4，a_4，a_4，b_3，b_3，b_3，b_4 \ n \ n c n r \ in \ in c in c in。本文的目的是研究对系统非本地术语的影响，并在参数上找到明确的条件，使系统具有独特的全局有限解决方案。我们的结论定量表明，非本地竞争可以促进全球和统一的解决方案，而全球合作竞赛对系统的界限不利。那是： o如果$ a_3，a_4，b_3，b_4> 0 $，即，当$ n \ leq2 $时，有非局部内内和种间竞赛，那么对于任何正面参数，系统的解决方案均具有全球限制；当$ n \ geq3 $，合适的大$ A_1，B_2 $（本地种内比赛）确保没有爆炸。 o如果$ a_3，a_4，b_3，b_4 <0 $，即，有全球性内部和种间合作，那么对于任何$ n \ geq1 $，获得了$ a_1的清晰且宽敞的条件，b_2 $是获得了b_2 $，这使得系统允许系统解决方案。 此外，我们认为分别具有弱和强烈不对称竞争案例的空间均衡平衡的全球渐近稳定性。
This paper deals with the solution of following chemotaxis system with competitive kinetics and nonlocal terms \begin{eqnarray*} \left\{ \begin{array}{llll} u_t=d_1Δu-χ_1\nabla\cdot(u\nabla w)+u\left(a_0-a_1u-a_{2}v-a_3\int_Ωu-a_4\int_Ωv\right), &x\in Ω, t>0,\\ v_t=d_2Δv-χ_2\nabla\cdot(v\nabla w)+v\left(b_0-b_1u-b_{2}v-b_3\int_Ωu-b_4\int_Ωv\right), &x\in Ω, t>0,\\ w_t=d_3Δw-λw+k u+l v, &x\inΩ, t>0, \end{array} \right. \end{eqnarray*} in a smoothly bounded domain $Ω\subset \mathbb{R}^N, N\geq1$, where $a_0, a_1, a_2, b_0, b_1, b_2>0$ and $a_3, a_4, b_3, b_4\in\mathbb{R}$. The purpose of this paper is to investigate the impact on nonlocal terms of the system, and to find clear conditions on parameters such that the system possesses a unique global bounded solution. Our conclusion quantitatively suggests that the nonlocal competitions can contribute to global and uniformly bounded solutions, while the global cooperations are adverse to boundedness of system. That is: o If $a_3, a_4, b_3, b_4>0$, i.e., there are nonlocal intraspecific and interspecific competitions, when $N\leq2$, then for any positive parameters the solution of system is globally bounded; when $N\geq3$, suitable large $a_1, b_2$ (local intraspecific competitions) ensure there is no blowup. o If $a_3, a_4, b_3, b_4<0$, i.e., there are globally intraspecific and interspecific cooperations, then for any $N\geq1$, a clear and largeness condition on $a_1, b_2$ is obtained which makes the system admits a boundedness solution. Furthermore, we consider the globally asymptotically stability of spatially homogeneous equilibrium with weak and strongly asymmetric competition cases, respectively.
