含非局部项的两物种趋化模型的渐近动力学
偏微分方程分析
2017-05-17 v3
摘要
本研究考虑以下具有非局部项的双物种抛物-抛物-椭圆型扩展吸引趋化系统 { u t = d 1 Δ u − χ 1 ∇ ( u ⋅ ∇ w ) + u ( a 0 − a 1 u − a 2 v − a 3 ∫ Ω u − a 4 ∫ Ω v ) , x ∈ Ω v t = d 2 Δ v − χ 2 ∇ ( v ⋅ ∇ w ) + v ( b 0 − b 1 u − b 2 v − b 3 ∫ Ω u − b 4 ∫ Ω v ) , x ∈ Ω 0 = d 3 Δ w + k u + l v − λ w , x ∈ Ω \begin{cases} u_t=d_1\Delta u-\chi_1\nabla (u\cdot \nabla w)+u\left(a_0-a_1u-a_2v-a_3\int_{\Omega}u-a_4\int_{\Omega}v\right),\quad x\in \Omega \quad\cr v_t=d_2\Delta v-\chi_2\nabla (v\cdot \nabla w)+v\left(b_0-b_1u-b_2v-b_3\int_{\Omega}u-b_4\int_{\Omega}v\right),\quad x\in \Omega \quad\cr 0=d_3\Delta w+k u+lv-\lambda w,\quad x\in \Omega \quad\cr \end{cases} ⎩ ⎨ ⎧ u t = d 1 Δ u − χ 1 ∇ ( u ⋅ ∇ w ) + u ( a 0 − a 1 u − a 2 v − a 3 ∫ Ω u − a 4 ∫ Ω v ) , x ∈ Ω v t = d 2 Δ v − χ 2 ∇ ( v ⋅ ∇ w ) + v ( b 0 − b 1 u − b 2 v − b 3 ∫ Ω u − b 4 ∫ Ω v ) , x ∈ Ω 0 = d 3 Δ w + k u + l v − λ w , x ∈ Ω Ω ⊂ R n ( n ≥ 1 ) \Omega \subset \mathbb{R}^n(n\ge1) Ω ⊂ R n ( n ≥ 1 ) a 0 , b 0 , a 1 , a_0,b_0,\, \,a_1, a 0 , b 0 , a 1 , b 2 b_2 b 2 a 2 , a 3 , a 4 , b 1 , b 3 , a_2,\, a_3, \, a_4, \, b_1,\, b_3, a 2 , a 3 , a 4 , b 1 , b 3 , b 4 b_4 b 4 a i , b i , d i , l , k , λ a_i,\, b_i,d_i,l,k,\lambda a i , b i , d i , l , k , λ χ i \chi_i χ i a i , b i , d i , l , k , λ a_i,\, b_i,d_i,l,k,\lambda a i , b i , d i , l , k , λ χ i \chi_i χ i
引用
@article{arxiv.1701.03235,
title = {Asymptotic dynamics in a two-species chemotaxis model with non-local terms},
author = {Tahir Bachar Issa and Rachidi Bolaji Salako},
journal= {arXiv preprint arXiv:1701.03235},
year = {2017}
}