论文标题
具有均方性耗散项的微分方程系统的灭绝时间附近的行为
Behavior near the extinction time for systems of differential equations with sublinear dissipation terms
论文作者
论文摘要
本文的重点是具有sublinear耗散项的普通微分方程系统解决方案解决方案的灭绝时间。假设耗散术语是线性映射$ a $和一个均匀的标量函数$ h $ a负度$-α$的产物。然后，任何具有灭绝时间的解决方案$ t _*$的行为都像$（t _* - t）^{1/α}ξ_*$作为时间$ t \ to t _*^ - $，其中$ξ_*$是$ a $的特征。结果允许高阶项为一般，而非线性函数$ h $采用非常复杂的表格。作为演示，我们的理论研究应用于不均匀的人群模型。
This paper is focused on the behavior near the extinction time of solutions of systems of ordinary differential equations with a sublinear dissipation term. Suppose the dissipation term is a product of a linear mapping $A$ and a positively homogeneous scalar function $H$ of a negative degree $-α$. Then any solution with an extinction time $T_*$ behaves like $(T_*-t)^{1/α}ξ_*$ as time $t\to T_*^-$, where $ξ_*$ is an eigenvector of $A$. The result allows the higher order terms to be general and the nonlinear function $H$ to take very complicated forms. As a demonstration, our theoretical study is applied to an inhomogeneous population model.
