8 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…