Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow (Q1772492)

The authors compute the explicit solution of the minimizing total variation flow in \(\mathbb{R}^2\) given by the equation \[ {\partial u\over\partial t}= \text{div}\Biggl({Du\over|Du|}\Biggr)\quad\text{in }Q_T= (0,T)\times \mathbb{R}^2 \] together with the initial datum \(u(0,x)= \sum^m_{i=1} b_i\chi_{C_i}(x)\), where \(b_i\in\mathbb{R}\) and \(C_i\) are bounded convex sets in \(\mathbb{R}^2\), which are sufficiently far apart. The paper also contains numerical examples of evolutions.