Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow
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.
scientific article; zbMATH DE number 2157848