非齐次次扩散方程的严格正性性质及其在耦合次扩散系统中的应用
Strict positivity property of inhomogeneous subdiffusion equations and its application to coupled subdiffusion systems
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中文总结 AI 辅助
研究非齐次次扩散方程的严格正性性质，通过连接格林函数填补缺失的严格正性。作为应用，研究耦合次扩散系统的严格正性，在适当条件下其不仅在时间上传播，还在系统分量间传播，为理解正性性质提供统一框架。
中文摘要 AI 辅助
次扩散方程解的正性已被广泛研究，主要针对单个方程的齐次问题。本文通过特殊函数连接分数阶和经典扩散方程的格林函数，填补了具有非负且非平凡源项的非齐次次扩散方程缺失的严格正性。作为直接应用，进一步研究了具有非负且部分非平凡初值或源的耦合次扩散系统的严格正性性质。在适当的合作性和连通性条件下，严格正性不仅在时间上传播，还在系统不同分量间传播，反映了耦合结构引起的内在相互作用。这些结果为理解标量和耦合次扩散方程的正性性质提供了统一框架，提供了超越经典极大值原理方法的新见解。
英文摘要
The positivity of solutions to subdiffusion equations has been widely studied, mainly in the context of homogeneous problems for single equations. In this article, we fill the missing strict positivity for inhomogeneous subdiffusion equations with nonnegative and nontrivial source terms by connecting Green's functions for fractional and classical diffusion equations via special functions. As a direct application, we further investigate the strict positivity property of coupled subdiffusion systems with nonnegative and partially nontrivial initial values or sources. Under suitable cooperativeness and connectivity conditions, the strict positivity turns out to propagate not only in time but also across different components of the system, reflecting the intrinsic interactions induced by the coupling structure. These results provide a unified framework for understanding positivity properties of both scalar and coupled subdiffusion equations, offering new insights beyond the classical maximum principle approach.
