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Boundedness criteria for a chemotaxis consumption model with gradient nonlinearities
Alessandro Columbu
This work deals with the consumption chemotaxis problem \begin{equation*} \begin{cases*} u_t = Δu - χ\nabla \cdot u\nabla v + λu - μu^2 - c \lvert \nabla u \rvert^γ, & \text{in $Ω\…
Global existence and lower bounds in a class of tumor-immune cell interactions chemotaxis systems
Shanmugasundaram Gnanasekaran, Alessandro Columbu, Rafael Díaz Fuentes +1
This paper investigates the properties of classical solutions to a class of chemotaxis systems that model interactions between tumor and immune cells. Our focus is on examining the…
Uniform-in-time boundedness in a class of local and nonlocal nonlinear attraction-repulsion chemotaxis models with logistics
Alessandro Columbu, Rafael Diaz Fuentes, Silvia Frassu
This article deals with a class of chemotaxis systems describing mechanisms from mathematical biology. In the specific, for a rather general class of attraction-repulsion models, w…
Properties of given and detected unbounded solutions to a class of chemotaxis models
Alessandro Columbu, Silvia Frassu, Giuseppe Viglialoro
This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction-repulsion model, with nonlinear productions, diffusion, s…
Some refined criteria toward boundedness in an attraction-repulsion chemotaxis system with nonlinear productions
Alessandro Columbu, Silvia Frassu, Giuseppe Viglialoro
We study some zero-flux attraction-repulsion chemotaxis models, with nonlinear production rates for the chemorepellent and the chemoattractant. This paper partially improves some k…