Chemotactic collapse in a parabolic system of mathematical biology

In 1970, Keller and Segel proposed a parabolic system describing the chemotactic feature of cellular slime molds and recently, several mathematical works have been devoted to it.In the present paper, we study its blowup mechamism and prove the following.First, chemotactic collapse occurs at each isolated blowup point.Next, any blowup point is isolated, provided that the Lyapunov function is bounded from below.Finally, only the origin can be a blowup point of radially symmetric solutions.