Global Conference on Mathematics and Applications (GCMA)

Spatial heterogeneity and time-dependent interfaces play a critical role in the persistence and distribution of populations in ecological and epidemiological systems. In this work, we extend classical reaction–diffusion models to heterogeneous domains separated by moving interfaces with dynamic transmission conditions. We establish the well-posedness of the resulting system using maximal Lp-regularity theory and illustrate the influence of spatial heterogeneity, interface evolution, and asymmetric fluxes through numerical simulations. The proposed framework is applicable to arbitrary spatial dimensions and provides insights into population persistence, spatial spread, and stability thresholds in complex environments.