For the planar and spatial N-body problems, it has been proved by Marchal and Chenciner that solutions for the minimizing problem with fixed ends are free from interior collisions. This important result has been extended by Ferrario-Terracini to Newtonian-type problems and equivariant problems, and has been used to construct many symmetric solutions for the Nbody problem. In this paper we are i...

In this paper, we prove the leading term of time-asymptotics moving vacuum boundary for compressible inviscid flows with damping to be that Barenblatt self-similar solutions corresponding porous media equations obtained by simplifying momentum via Darcy’s law plus possible shift due movement center mass, in one-dimensional and three-dimensional spherically symmetric motions, respectively. This ...

Abstract A delayed reaction-diffusion system with free boundaries is investigated in this paper to understand how the bacteria spread spatially larger area from initial infected habitat. Under assumptions that nonlinearities are of monostable type and values satisfy some compatible condition, we show boundary problem well-posed discuss long-time behaviour solution (including spreading vanishing...