Hyperbolic mean curvature flow with a forcing term: Evolution of plane curves

In this paper we study the evolution of closed strictly convex plane curves moving by the hyperbolic mean curvature flow with a forcing term. It is shown that the flow admits a unique short-time smooth solution and the convexity of the curves is preserved during the evolution. When the forcing term is a negative constant, we prove the curves either converge to a point or a C0C0 curve. For a positive constant forcing term, the flow has a unique smooth solution in any finite time and expands to infinity as tt tends to infinity if the initial curvature is smaller than MM, the flow will blow up in a finite time if the initial curvature is larger than MM.