论文标题
一维本地和部分消散双曲系统的衰减
On the decay of one-dimensional locally and partially dissipated hyperbolic systems
论文作者
论文摘要
我们研究了部分耗散的线性双曲系统的时间 - 肿瘤行为，该系统位于域的合适子集中。更准确地说，我们恢复了满足稳定性条件（SK）的部分耗散系统的经典衰减速率，仅取决于每个组件的速度和未阻尼区域的大小。为了量化这一延迟，我们假设未阻尼区域是一个有界的空间间隔，并且在耗散上没有空间限制的系统满足稳定性条件（SK）。前者的假设可确保系统在未阻尼区域的特征所花费的时间是有限的，而后者是每当阻尼活跃的溶液衰减时。我们的方法包括将系统重新构成非耦合的传输方程，并表明时间范围的估计值被每个特征在未阻尼区域所花费的时间的总和延迟。
We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the classical decay rates of partially dissipative systems satisfying the stability condition (SK) with a time-delay depending only on the velocity of each component and the size of the undamped region. To quantify this delay, we assume that the undamped region is a bounded space-interval and that the system without space-restriction on the dissipation satisfies the stability condition (SK). The former assumption ensures that the time spent by the characteristics of the system in the undamped region is finite and the latter that whenever the damping is active the solutions decay. Our approach consists in reformulating the system into n coupled transport equations and showing that the time-decay estimates are delayed by the sum of the times each characteristics spend in the undamped region.
