A general paradigm of binary phase-segregation processes through the lens of four critical mechanisms

We investigate a nonlocal nonlinear parabolic equation that characterizes phase-segregation phenomena in a binary system, influenced by four distinct mechanisms. These mechanisms offer full user control over both the temporal and spatial scales of the phase separation process within a bounded measurable subset of $ \mathbb{R}^{d} $, $ d\geq 1. $ We establish well-posedness results and examine regularity across various scenarios, encompassing both smooth and singular entropy density potentials. Additionally, we complement our theoretical findings with numerical simulations and physical experiments, which elucidates the intricate interplay of the four-point physical mechanism underlying the phase segregation process.