Alzheimer’s disease (AD) is a neurodegenerative disorder with multifactorial etiology that poses a serious threat to human health. This work is devoted to a stochastic reaction–diffusion system for AD with space–time white noise accounting, which describes the positive feedback loop among the A$\beta$ and the Ca^2＋. The existence and uniqueness of mild solutions for the system are obtained by using the truncation method. Then, we study the long-time behaviors of the system. Further, an illustrative example is shown to support the obtained analytic results.

中文翻译：

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时空白噪声驱动的随机反应-扩散阿尔茨海默病系统分析

阿尔茨海默病 (Alzheimer's disease, AD) 是一种具有多因素病因的神经退行性疾病，对人类健康构成严重威胁。这项工作致力于研究具有时空白噪声计算的 AD 的随机反应扩散系统，该系统描述了 A 之间的正反馈回路$\beta$和Ca ^2＋。利用截断法得到系统温和解的存在性和唯一性。然后，我们研究了系统的长期行为。此外，显示了一个说明性示例以支持所获得的分析结果。