| Abstract: |
| In this talk, we will review the main results concerning hyperbolic Cauchy problems in which the family of generators associated with the system is time-dependent. In particular, we will discuss the uniqueness of weak solutions and their relationship with mild and classical solutions. As a concrete application motivated by pattern formation in semi-arid ecosystems, we will address a non-homogeneous ecological model coupling non-local biomass dispersion (higher-order spatial operators) with a Cattaneo-type delayed resource flow. We will highlight how our theoretical framework ensures the well-posedness of such strongly coupled systems even when all ecological and physical parameters vary continuously with time, reflecting seasonal forcing and climatic variations. |
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