当前位置: X-MOL 学术Appl. Math. Lett. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Boundedness of solutions to a parabolic attraction–repulsion chemotaxis system in R2: The attractive dominant case
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2021-04-28 , DOI: 10.1016/j.aml.2021.107354
Toshitaka Nagai , Yukihiro Seki , Tetsuya Yamada

We discuss the Cauchy problem for a parabolic attraction–repulsion chemotaxis system: tu=Δu(β1uv1)+(β2uv2),t>0,xR2,tvj=Δvjλjvj+u,t>0,xR2(j=1,2),u(0,x)=u0(x),vj(0,x)=vj0(x),xR2(j=1,2)with positive constants βj,λj>0 (j=1,2) satisfying β1>β2. In our companion paper, the authors proved the existence of global-in-time solutions for any initial data with (β1β2)R2u0dx<8π. In this paper, we prove that every solution stays bounded as t provided that (β1β2)R2u0dx<4π.



中文翻译:

一类抛物线吸引-排斥趋化系统解的有界性。 [R2个:有吸引力的主导案例

我们讨论抛物线-排斥趋化系统的柯西问题: Ťü=Δü-β1个üv1个+β2个üv2个Ť>0X[R2个ŤvĴ=ΔvĴ-λĴvĴ+üŤ>0X[R2个Ĵ=1个2个ü0X=ü0XvĴ0X=vĴ0XX[R2个Ĵ=1个2个具有正常数 βĴλĴ>0 Ĵ=1个2个 满意的 β1个>β2个。在我们的伴随论文中,作者证明了存在任何具有以下问题的初始数据的全局及时解决方案的存在:β1个-β2个[R2个ü0dX<8π。在本文中,我们证明了每个解决方案在Ť 规定 β1个-β2个[R2个ü0dX<4π

更新日期:2021-05-11
down
wechat
bug