2 papers
math.AP2024
A few topics on total variation flows
Yoshikazu Giga, Hirotoshi Kuroda, Michał Łasica
Total variation gradient flows are important in several applied fields, including image analysis and materials science. In this paper, we review a few basic topics including defini…
math.AP2014
Analysis of solutions to a model parabolic equation with very singular diffusion
Michał Łasica
We consider a singular parabolic equation of form \[ u_t = u_{xx} + \fracα{2}(\mathrm{sgn}\,u_x)_x \] with periodic boundary conditions. Solutions to this kind of equations exhibit…