论文标题
通过有吸引力的过渡，在具有种群通量的扩散捕食者模型中的全球存在和稳定
Global existence and stabilization in a diffusive predator-prey model with population flux by attractive transition
论文作者
论文摘要
扩散的Lotka-Volterra Predator-Prey模型\ begin {eqnarray*} \ left \ {\ oken {array} {rcll} {rcll} u_t＆=＆=＆\ nabla \ cdot \ cdot \ cdot \ cdot \ left [d_1 \ nabla u +χv^2 \χv^2 \χv^2 \ Nabla \ big（\ dfrac {u} {v} \ big）\ right]+u（m_1-u+av），\ qquad＆x \inΩ，\ t> 0，\\ v_t＆=＆d_2ΔV+v（m_2-bu-v），\ qquad＆xquad＆xquad＆x \ ince \ t> 0，\ t> 0。在Neumann边界条件下，在一个有限域$ω\ subset \ subset \ MathBb {r}^n $，$ n \ in \ {2,3 \} $中，考虑到在有限的域$ω\ subset \ subset \ subset \ subset \ subset \ subset \ subset \ subset \ subset \ subset \ subset \ subset \ subset*} $，其中$ d_1，d_1，d_2，m_1，m_1，b $是正常数是一个不变的常数。本文的目的是在情况下建立经典解决方案的全球存在和界限，并在此情况下$ n = 2 $以及全球存在的解决方案存在$ n = 3 $，并显示长期稳定。更准确地说，我们证明了解决方案$（u（\ cdot，t），v（\ cdot，t））$将$（u_*，v _*）$作为$ t \ to \ infty $收集到恒定稳态$（u_*，v _*） $ u _*（m_1-u _*+av _*）= v _*（m_2-bu _* - v _*）= 0 $ with $ u_*> 0 $（涵盖共依性以及猎物延迟案例）。
The diffusive Lotka-Volterra predator-prey model \begin{eqnarray*} \left\{ \begin{array}{rcll} u_t &=& \nabla\cdot \left[ d_1\nabla u + χv^2 \nabla \Big(\dfrac{u}{v}\Big)\right] +u(m_1-u+av), \qquad & x\inΩ, \ t>0, \\ v_t &=& d_2Δv+v(m_2-bu-v), \qquad & x\inΩ, \ t>0, \end{array} \right. \end{eqnarray*} is considered in a bounded domain $Ω\subset\mathbb{R}^n$, $n \in\{2,3\}$, under Neumann boundary condition, where $d_1, d_2, m_1, χ, a, b$ are positive constants and $m_2$ is a real constant. The purpose of this paper is to establish global existence and boundedness of classical solutions in the case $n=2$ and global existence of weak solutions in the case $n=3$ as well as show long-time stabilization. More precisely, we prove that the solutions $(u(\cdot,t), v(\cdot,t))$ converge to the constant steady state $(u_*, v_*)$ as $t \to \infty$, where $u_*, v_*$ solves $u_*(m_1-u_*+av_*)=v_*(m_2-bu_*-v_*)=0$ with $u_* > 0$ (covering both coexistence as well as prey-extinction cases).
