1. Introduction. The purpose of the present paper is to study blowup mechanism for a system of parabolic equations. It arises in mathematical biology to describe the chemotactic feature of slime molds.We take the form proposed by Nanjundiah [20], simplifying the one previously given by Keller and Segel [14]. It is stated as follows, where u = u (x, t) and v = v(x, t) stand the density of slime molds and the concentration chemical substances secreted by them, respectively:

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We study a parabolic-elliptic system of partial differential equations, which describes the chemotactic feature of slime molds. It is known that the blowup solution forms singularities such as delta functions, referred to as the collapses. Here, we study the case that the domain is a flat torus and show that the post-blowup continuation of the solution is possible only when those collapses are quantized with the mass 8p.

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