Motion of interfaces for a damped hyperbolic Allen-Cahn equation

This paper concerns with the motion of the interface for a damped hyperbolic Allen-Cahn equation, in a bounded domain of Rn, for n = 2 or n = 3. In particular, we focus the attention on radially symmetric solutions and extend to the hyperbolic framework some well-known results of the classic parabolic case: it is shown that, under appropriate assumptions on the initial data and on the boundary conditions, the interface moves by mean curvature as the diffusion coecient goes to 0.