1 citations · 2 across the 9 of their papers we have counts for
9 papers
Numerical stationary states for nonlocal Fokker-Planck equations via fixed points of consistency maps
José A. Carrillo, Yurij Salmaniw, Antonio León Villares
We propose a fixed-point-based numerical framework for computing stationary states of nonlocal Fokker-Planck-type equations. Instead of discretising the differential operators dire…
Learning functional components of PDEs from data using neural networks
Torkel E. Loman, Yurij Salmaniw, Antonio Leon Villares +2
Partial differential equation (PDE) models frequently contain unknown functional terms that cannot be measured directly, limiting their predictive utility. While data-driven method…
Long-time behaviour and bifurcation analysis of a two-species aggregation-diffusion system on the torus
José A. Carrillo, Yurij Salmaniw
We investigate stationary states, including their existence and stability, in a class of nonlocal aggregation-diffusion equations with linear diffusion and symmetric nonlocal inter…
Dynamics of a coupled nonlocal PDE-ODE system with spatial memory: well-posedness, stability, and bifurcation analysis
Yurij Salmaniw, Di Liu, Junping Shi +1
Nonlocal aggregation-diffusion models, when coupled with a spatial map, can capture cognitive and memory-based influences on animal movement and population-level patterns. In this…
Structural identifiability of linear-in-parameter parabolic PDEs through auxiliary elliptic operators
Yurij Salmaniw, Alexander P Browning
Parameter identifiability is often requisite to the effective application of mathematical models in the interpretation of biological data, however theory applicable to the study of…
Well-posedness of aggregation-diffusion systems with irregular kernels
José A. Carrillo, Yurij Salmaniw, Jakub Skrzeczkowski
We consider aggregation-diffusion equations with merely bounded nonlocal interaction potential . We are interested in establishing their well-posedness theory when the nonlocal…
From habitat decline to collapse: a spatially explicit approach connecting habitat degradation to destruction
Yurij Salmaniw, Zhongwei Shen, Hao Wang
Habitat loss, driven primarily by anthropogenic activity, significantly threatens ecosystem sustainability. While it is well understood that habitat loss is the leading contributor…
Biological Aggregations from Spatial Memory and Nonlocal Advection
Di Liu, Yurij Salmaniw, Jonathan R. Potts +2
We investigate a nonlocal single-species reaction-diffusion-advection model that integrates the spatial memory of previously visited locations and nonlocal detection in space, resu…
Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping
Hao Wang, Yurij Salmaniw
The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that disting…