论文标题
部分可观测时空混沌系统的无模型预测
Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior
论文作者
论文摘要
由于与抛物线方程的最显着差异，解决方案的长期或短期行为对时间分数进化方程是由分数订单主导的，分数订单的独特确定经常在文献中进行研究。与所有现有结果不同，在本文中，我们仅通过单个空间点附近$ t = 0 $的渐近扩展的主要条款证明了订单和参数的唯一性（后者的乘数最多）。此外，我们发现了关于观察数据巧合的未知初始值或源术语的特殊条件。作为副产品，我们甚至可以通过相同的数据结论初始值或源项的唯一性。证明依赖于采取拉普拉斯变换后的渐近膨胀和广义征收功能的完整性。
As the most significant difference from parabolic equations, long-time or short-time behavior of solutions to time-fractional evolution equations is dominated by the fractional orders, whose unique determination has been frequently investigated in literature. Unlike all the existing results, in this article we prove the uniqueness of orders and parameters (up to a multiplier for the latter) only by principal terms of asymptotic expansions of solutions near $t=0$ at a single spatial point. Moreover, we discover special conditions on unknown initial values or source terms for the coincidence of observation data. As a byproduct, we can even conclude the uniqueness for initial values or source terms by the same data. The proof relies on the asymptotic expansion after taking the Laplace transform and the completeness of generalized eigenfunctions.
