2024/01/30 by Yoshikazu Giga, Giga, Yoshikazu, Hirotoshi Kuroda +3
Engineering · Economics, Econometrics and Finance · Computer Science · #Reservoir Engineering and Simulation Methods #Stochastic processes and financial applications #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2401.17179
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 definition of a solution, explicit examples and the notion of calibrability, finite time extinction, and some regularity properties of solutions. We focus on the second-order flow (possibly with weights) and the fourth-order flow. We also discuss the fractional cases.