Global existence and asymptotic behavior of the fractional chemotaxis system with signal-dependent sensitivity

Abstract

In this paper, we study a fractional chemotaxis model with signal-dependent sensitivity and the source term, which involves two parabolic equations with fractional diffusions. We develop a suitable mathematical framework for a unified treatment of the existence and decay estimates. Based on an appropriate functional space, we show the existence, uniqueness and temporal decay of the global classical solutions to the problem simultaneously under the smallness initial assumptions.