On explicit lower bounds and blow-up times in a model of chemotaxis

Abstract. This paper is concerned with a parabolic Keller-Segel system in R^n, with n = 2 and 3, under Neumann boundary conditions on the boundary. Firstly important theoretical and general results dealing with lower bounds for blow-up time estimates are summarized and analyzed. Secondly, a resolution method is proposed and used to both compute the real blow-up times of such unbounded solutions and analyze and discuss some of their properties