Abstract
ABSTRACT In this paper, we consider the zero-flux chemotaxis system in a smooth and bounded domain Ω of . The chemotactic sensitivity χ is a general nonnegative function from while g, the production of the chemical signal v, belongs to and satisfies , for all , and It is established that no chemotactic collapse for the cell distribution u occurs in the sense that any arbitrary nonnegative and sufficiently regular initial data emanates a unique pair of global and uniformly bounded functions which classically solve the corresponding initial boundary value problem. Finally, we illustrate the range of dynamics present within the chemotaxis system by means of numerical simulations.
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