论文标题
长期渐近估计和时间分数波方程的相关逆源问题
Long-time asymptotic estimate and a related inverse source problem for time-fractional wave equations
论文作者
论文摘要
位于传统的抛物线和双曲线方程之间，订单$α\ in（1,2）$ in Time的时间折叠波方程继承了衰减和振荡性能。在本文中，我们为均质时折叠方程建立了长期的渐近估计，这很容易暗示在某些符号条件下，在初始值的某些标志条件下，解决方案对解决方案的严格阳性/负率。作为直接应用程序，我们证明了确定时间组件时相关逆源问题的唯一性。
Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order $α\in(1,2)$ in time inherit both decaying and oscillating properties. In this article, we establish a long-time asymptotic estimate for homogeneous time-fractional wave equations, which readily implies the strict positivity/negativity of the solution for $t\gg1$ under some sign conditions on initial values. As a direct application, we prove the uniqueness for a related inverse source problem on determining the temporal component.
