Mathematical analysis of the spatiotemporal concentration of growth inhibitory factor in multicellular spheroids tumour

In this work, we look at spatially dependent diffusion of growth inhibitory factor (GIF) in multicell spheroids. The production GIF is taken to be time-dependent and heterogeneous within the spheroid. Using a semigroup approach, investigate dynamical behaviour presented mathematical model. Firstly, existence positivity solutions. Secondly, with time-independent source GIF, prove unique steady state which asymptotically stable. Moreover, (asymptotically) (almost) periodic supply show solution that defines global attractor.