Local and Global Existence for Non-local Multi-Species Advection-Diffusion Models

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

  • Date created
  • Subjects / Keywords
  • Type of Item
    Article (Draft / Submitted)
  • DOI
  • License
    Attribution-NonCommercial 4.0 International