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Global boundedness in a chemotaxis quasilinear parabolic predator–prey system with pursuit-evasion
Nonlinear Analysis: Real World Applications ( IF 1.8 ) Pub Date : 2020-12-05 , DOI: 10.1016/j.nonrwa.2020.103269
Bruno Telch

We analyze some configurations of the general chemotaxis predator–prey model with pursuit-evasion dynamics tu(Fu(u)u)+(Fp(u)p)=uF1(w)F2(u)tw(Fw(w)w)(Fq(w)q)=wF3(w)δuwin Ω×(0,T) with Neumann boundary condition and non-negative initial data, where p and q are the predator’s and the prey’s pheromone, respectively, modeled by parabolic or elliptic equations, and ΩRd, with d1, is a smooth bounded domain. We assume Fu and Fw to be smooth positive functions satisfying kusp1Fu(s) and kwsp2Fw(s) when ss0>1, Fp,Fq smooth non-negative functions such that kp1sp0Fp(s)kp1sp0 when ss0 and Fq(s)kqsq0 for all s0, with q0=1 or q02. We also assume F1,F2 and F3 to be smooth with F1(0)=F2(0)=F3(0)=0, F20, F1(s)k1sθ, F2(s)k2s1+b, b0, F3(s)k3k4sa, for ss0, a>0, k30, k4>0. We prove that for θ,a,b,q0 and p0 satisfying some relation there exists a unique classical solution to the system which is global in time and bounded. The result in independent on p1,p2R.



中文翻译:

具有追逃性的趋化拟线性抛物线捕食者-被捕食系统的整体有界性

我们利用逃避动力学分析了一般趋化性捕食-被捕食模型的一些结构 Ťü-Füüü+Fpüp=üF1个w-F2üŤw-Fwww-Fqwq=wF3w-δüwΩ×0Ť 带有Neumann边界条件和非负初始数据,其中 pq 是分别由抛物线或椭圆方程建模的掠食者和猎物的信息素,以及 Ω[Rd,带有 d1个是平滑的有界域。我们猜测FüFw 使人满意的积极作用 ķüsp1个Füsķwsp2Fws 什么时候 ss0>1个FpFq 使非负函数平滑,从而 ķp1个sp0Fpsķp1个sp0 什么时候 ss0Fqsķqsq0 对所有人 s0,带有 q0=1个 要么 q02。我们还假设F1个F2F3F1个0=F20=F30=0F20F1个sķ1个sθF2sķ2s1个+bb0F3sķ3-ķ4s一种,对于 ss0一种>0ķ30ķ4>0。我们证明θ一种bq0p0满足某种关系,该系统存在一个独特的经典解决方案,该解决方案在时间上是全局的并且是有界的。结果独立p1个p2[R

更新日期:2020-12-05
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