Dr Yurij Salmaniw

Nonlinear partial differential equations; mathematical biology; spatial ecology; animal movement; reaction–diffusion equations; aggregation–diffusion equations; nonlocal models; PDE–ODE systems; habitat degradation; habitat destruction; habitat fragmentation; cognitive movement; perception; memory; learning; pattern formation; bifurcation theory; spectral theory; long-time behaviour; steady states; numerical methods for PDEs; numerical continuation; parameter identifiability; data-informed modelling.

Summary of Research Project(s)

At Sheffield, Yurij's Leverhulme Early Career Fellowship project develops nonlinear PDE models for animal movement, space use, and population persistence in changing landscapes. Working with Prof. Jonathan Potts, I study how movement mechanisms such as perception, memory, learning, and nonlocal sensing interact with environmental structure, including habitat degradation, destruction, fragmentation, corridors, and patch geometry.

The project has two closely linked strands. The first develops and analyses nonlocal aggregation–diffusion models for movement and interaction, with emphasis on well-posedness, steady states, bifurcation structure, and the role of cognitive/spatial maps. The second studies reaction–diffusion models for habitat loss and fragmentation, connecting analytical and numerical results to experimental systems and ecological data. Together, these strands aim to identify general mathematical principles for how individual-level movement behaviour and landscape-scale structure shape spatial distributions, species persistence, and ecological responses to habitat change.