Blowup And Self-similar Solutions For N-component Drift-diffusion Systems

We discuss asymptotic properties of solutions of three-component parabolic drift–diffusion systems coupled through an elliptic equation in two space dimensions.In particular,conditions for finite time blowup versus the existence of forward self-similar solutions are studied by using the fundamental solution,the integral method and the invariant property of the solution.For the gravitational system,electric system,K-O system and repulsion system,we obtain the corresponding blowup conditions.For gravitational system and K-O system,we obtain the corresponding conditions of existence of self-similar solutions.Also,we generalized to the n-component parabolic drift-diffusion systems coupled through an elliptic equation in two space dimensions.Conditions for finite time blowup versus the existence of forward self-similar solutions are studied.For the gravitational system,electric system,K-O system and repulsion system,we obtain the corresponding blowup conditions.For gravitational system and K-O system,we obtain the corresponding conditions of existence of self-similar solutions.