Self-similar solutions to a parabolic system modeling chemotaxis

We study the forward self-similar Solutions to a parabolic system modeling chemotaxis u(t) = del (.) (delu - udelv), tauv(t) = delv + u in the whole space R-2, where tau is a positive constant. Using the Liouville-type result and the method of moving planes, it is proved that self-similar solutions (u, v) must be radially symmetric about the origin. Then the structure of the set of self-similar solutions is investigated. As a consequence, it is shown that there exists a threshold in f(R2)u for the existence of self-similar solutions. In particular, for 0 < tau less than or equal to 1/2, there exists a self-similar solution (u, v) if and only if integral(R2) u < 8pi. (C) 2002 Elsevier Science (USA).