Wave equation is a commonly used tool for describing various kinds of wave phenomena in nature such as sound wave, water wave, electromagnetic wave and string vibration. It is a second-order partial differential equation and describe the wave propagation without noises. However, real world is filled with noises everywhere. So deterministic wave equation is not enough to model some problems with additive noises. As a remedy method, stochastic wave equation driven by Wiener process was presented where the noise is considered random and modeled by using Wiener process. Except for randomness, uncertainty associated belief degrees is another different type of indeterministic phenomenon. For modeling the wave phenomena with uncertain noises, this paper aims at deriving an uncertain wave equation driven by Liu process, which is a type of partial differential equation. Here, Liu process is a Lipschitz continuous uncertain process with stationary and independent increments. Then, we prove the existence and uniqueness of the solution of an uncertain wave equation. Additionally, we give the inverse uncertainty distribution of a solution of an uncertain wave equation.

中文翻译：

---

振动弦的不确定波动方程


波动方程是描述声波、水波、电磁波、弦振动等自然界各种波动现象的常用工具。它是一个二阶偏微分方程，描述无噪声的波传播。然而，现实世界到处都充满了噪音。因此，确定性波动方程不足以模拟一些带有加性噪声的问题。作为一种补救方法，提出了由维纳过程驱动的随机波动方程，其中噪声被认为是随机的并使用维纳过程进行建模。除了随机性之外，与置信度相关的不确定性是另一种不同类型的非确定性现象。为了对具有不确定噪声的波动现象进行建模，本文旨在推导由刘过程驱动的不确定波动方程，这是一种偏微分方程。这里，Liu过程是一个具有平稳且独立增量的Lipschitz连续不确定过程。然后，我们证明了不确定波动方程解的存在性和唯一性。此外，我们还给出了不确定波动方程解的逆不确定性分布。