The initial value problem for a tissue growth mathematical model

This paper considers the initial value problem for a normal hyperbolic
curvature flow derived by the cell-based mathematical models of tissue
growth to account for the mechanistic influence of curvature on cell
evolution. The equations satisfied by support functions under this flow
is a hyperbolic Monge-Amp$\grave{e}$re equation. The
equation for both perimeter and area of closed curves under the flow are
also obtained. Based on this, we show that for a closed curve, if the
initial velocity $v_{0}<0$, the solution of this flow
converges to a point in finite time; if $v_{0}>0$, the
solution of this flow exists for all
$t\in[0,\infty)$.