Total Variation Flow and Sign Fast Diffusion in one dimension

快慢化学反应：Hamilton-Jacobi方程的收敛性与变分表示

Fast-slow chemical reactions: convergence of Hamilton-Jacobi equation and variational representation

本文研究一般化学反应在快慢尺度分离下的极限行为，通过粘性解一致收敛和变分表示的$Γ$-收敛，证明所有轨迹集中于慢流形，并由粗粒化RRE和HJE描述有效宏观动力学。

Total-Variation -- Fast Gradient Flow and Relations to Koopman Theory

The space-discrete Total Variation (TV) flow is analyzed using several mode decomposition techniques. In the one-dimensional case, we provide analytic formulations to Dynamic Mode Decomposition (DMD) and to Koopman Mode Decomposition (KMD) of the TV-flow and compare the obtained modes to TV spectral decomposition. We propose a computationally efficient algorithm to evolve the one-dimensional TV-flow. A significant speedup by three orders of magnitude is obtained, compared to iterative minimizations. A common theme, for both mode analysis and fast algorithm, is the significance of phase transit…

On the fast rotation asymptotics of a non-homogeneous incompressible MHD system

This paper is devoted to the analysis of a singular perturbation problem for a $2$-D incompressible MHD system with density variations and Coriolis force, in the limit of small Rossby numbers. Two regimes are considered. The first one is the quasi-homogeneous regime, where the densities are small perturbations around a constant state. The limit dynamics is identified as an incompressible homogeneous MHD system, coupled with an additional transport equation for the limit of the density variations. The second case is the fully non-homogeneous regime, where the densities vary around a general non…