Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models

Nonlocal advection is a key process in range of biological systems, from cells within individuals to the movement whole organisms. Consequently, recent years, there has been increasing attention on modeling non-local mathematically. These often take form partial differential equations, with integral terms nonlocality. One common formalism aggregation-diffusion equation, class advection-diffusion models nonlocal advection. This was originally used model single population but recently extended multispecies case way organisms may alter their presence coexistent species. Here we prove existence theorems for models, an arbitrary number We global $n=1$ spatial dimension and local $n>1$. describe efficient spectral method numerically solving these provide example simulation output. Overall, this helps solid mathematical foundation studying effect interspecies interactions space use.