7 papers
Learning functional components of PDEs from data using neural networks
Torkel E. Loman, Yurij Salmaniw, Antonio Leon Villares +2
Partial differential equations often contain unknown functions that are difficult or impossible to measure directly, hampering our ability to derive predictions from the model. Wor…
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…
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…
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…
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…
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…