论文标题
部分可观测时空混沌系统的无模型预测
Direct and inverse source problems for heat equation in quantum calculus
论文作者
论文摘要
在本文中，我们探讨了cauchy问题的弱解，以及在抽象希尔伯特（Hilbert）空间中提出的量子演算中热方程的逆源问题。为此，我们使用傅立叶系列扩展。此外，我们证明了逆问题的弱解决方案的存在，独特性和稳定性，并具有最终确定条件。我们提供了一些例子，例如Q-Sturm-Liouville问题，Q-Bessel操作员，Q呈现的Hamiltonian，分数Sturm-Liouville操作员以及我们分析的限制性分数Laplacian。
In this paper we explore the weak solutions of the Cauchy problem and an inverse source problem for the heat equation in the quantum calculus, formulated in abstract Hilbert spaces. For this we use the Fourier series expansions. Moreover, we prove the existence, uniqueness and stability of the weak solution of the inverse problem with a final determination condition. We give some examples such as the q-Sturm-Liouville problem, the q-Bessel operator, the q-deformed Hamiltonian, the fractional Sturm-Liouville operator, and the restricted fractional Laplacian, covered by our analysis.
