Blow-Up Profiles for a Semilinear Chemotaxis System Arising in Biology

Abstract

We consider the semilinear coupled system of parabolic-elliptic partial differential equations arising in chemotaxis involving forcing source of exponential growth type and homogeneous Dirichlet boundary conditions. The local existence and uniqueness of nonnegative classical solutions are proved. Also, a lower bound for the blow-up time if the solution blows up in finite time is derived. Moreover, the exponential decay of the associated energies are also studied. The results we obtained here essentially extend some existing results in this area.