Special Session 6: Propagation dynamics of PDEs: recent progress and trends

Infinite cascade of traveling waves in a nonlocal model of gravitational fingering
Iuliia Petrova
University of Sao Paulo (USP)
Brazil
Co-Author(s):    Sergey Tikhomirov
Abstract:
We introduce a new nonlocal model for gravitational fingering and study its wave propagation dynamics. Gravitational fingering is an instability in the displacement of miscible fluids in porous media, governed by Darcy's law, which occurs when a lighter fluid lies below a heavier one and gravity drives an exchange of positions. Our main result establishes the existence of a propagating terrace consisting of infinitely many traveling waves in a semi-discrete Transverse Flow Equilibrium (TFE) model. The talk is based on ongoing joint work with Sergey Tikhomirov (PUC-Rio, Brazil) and extends earlier results on two-tubes models of gravitational fingering (SIMA, arxiv:2401.05981)