Global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear production

Abstract

We study the global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth. We introduce superlinear production of a chemoattractant. We then show the global existence of solutions in $L_p$ space $( p > n )$ under certain relations between the degradation and production orders.