In this talk, we present a parabolic-elliptic system, which was proposed by Albi et al (2016) to describe the evolution of ion transport networks. Our first result asserts that the corresponding Neumann-Dirichlet initial-boundary value problem possesses a global weak solution for general large data in the two-dimensional setting. Our second result further reveals that such solution at least eventually becomes bounded and smooth, and approaches spatial equilibria in the large time limit.

会议密码:1005