This work is concerned with the gradient flow of absolutely p-homogeneous convex
functionals on a Hilbert space, which we show to exhibit finite (p< 2 p< 2) or infinite …

In this work we develop a nonlinear decomposition, associated with nonlinear
eigenfunctions of the p-Laplacian for p∈(1, 2). With this decomposition we can process …

Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is
essential for their analysis and modeling. In this work, we attempt to provide a consistent …

Implementation of nonlinear flows by explicit schemes can be very convenient, due to their
simplicity and low-computational cost per time step. A well known drawback is the small time …

Finding latent structures in data is drawing increasing attention in diverse fields such as fluid
dynamics, signal processing, and machine learning. Dimensionality reduction facilitates the …

This work binds the existence of Koopman Eigenfunction (KEF), the geometric of the
dynamics, and the validity of Dynamic Mode Decomposition (DMD) to one coherent theory …