Publications [#383254] of Alexander A. Kiselev

Papers Published

1. Kiselev, A; Sarsam, NA, Finite time blow-up in a 1D model of the incompressible porous media equation, Nonlinearity, vol. 38 no. 5 (May, 2025) [doi]
   (last updated on 2025/07/03)

   Abstract:
   We derive a PDE that models the behavior of a boundary layer solution to the incompressible porous media (IPM) equation posed on the 2D periodic half-plane. This 1D IPM model is a transport equation with a non-local velocity similar to the well-known Córdoba-Córdoba-Fontelos (CCF) equation. We discuss how this modification of the CCF equation can be regarded as a reasonable model for solutions to the IPM equation. Working in the class of bounded smooth periodic data, we then show local well-posedness for the 1D IPM model as well as finite time blow-up for a class of initial data.