L_p-Estimates of Solutions to n-Dimensional Parabolic-Parabolic System for Chemotaxis with Subquadratic Degradation

Abstract

We study the global existence of solutions to an n-dimensional parabolic-parabolic system for chemotaxis with a subquadratic degradation. We introduce sublinear 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.