Blowup in infinite time of radial solutions for a parabolic–elliptic system in high-dimensional Euclidean spaces

Abstract

We consider radial solutions blowing up in infinite time to a parabolic–elliptic system in N -dimensional Euclidean space. The system was introduced to describe the gravitational interaction of particles. In the case where N ≥ 2 , we can find positive and radial solutions blowing up in finite time. In the present paper, in the case where N ≥ 11 , we find positive and radial solutions blowing up in infinite time and investigate those blowup speeds, by using the so-called asymptotic matched expansion techniques and parabolic regularity.