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math.AP2025
Local well-posedness for a novel nonlocal model for cell-cell adhesion via receptor binding
Mabel Lizzy Rajendran, Anna Zhigun
Local well-posedness is established for a highly nonlocal nonlinear diffusion-adhesion system for bounded initial values with small support. Macroscopic systems of this kind were p…
math.AP2024
Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion
Maria Eckardt, Anna Zhigun
Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation fea…
math.AP2024
Global entropy solutions to a degenerate parabolic-parabolic chemotaxis system for flux-limited dispersal
Anna Zhigun
Existence of global finite-time bounded entropy solutions to a parabolic-parabolic system proposed in [16] is established in bounded domains under no-flux boundary conditions for n…