51 citations · 102 across the 15 of their papers we have counts for
17 papers
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…
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…
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…
Modelling non-local cell-cell adhesion: a multiscale approach
Anna Zhigun, Mabel Lizzy Rajendran
Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. duri…
Flux limitation mechanisms arising in multiscale modelling of cancer invasion
Anna Zhigun
Tumour invasion is an essential stage of cancer progression. Its main drivers are diffusion and taxis, a directed movement along the gradient of a stimulus. Here we review models w…
Multiphase modelling of glioma pseudopalisading under acidosis
Pawan Kumar, Christina Surulescu, Anna Zhigun
We propose a multiphase modeling approach to describe glioma pseudopalisade patterning under the influence of acidosis. The phases considered at the model onset are glioma, normal…