Vanishing layer thickness limit of convection in multilayer porous media

TL;DR

This paper studies the behavior of convection in multilayer porous media as one layer's thickness approaches zero, showing the solutions converge to a reduced model with fewer layers and analyzing the asymptotic behavior.

Contribution

It establishes the rigorous convergence of solutions and attractors in the vanishing layer thickness limit within the Darcy-Boussinesq framework.

Findings

Solutions converge strongly in L^2 as layer thickness tends to zero

Global attractors exhibit upper semi-continuity in the limit

Reduced model accurately describes the system when a layer vanishes

Abstract

Within the Darcy-Boussinesq framework for convection in multilayered porous media, we investigate the singular limit in which the thickness of one layer tends to zero. We establish that the solution of the full system converges to that of the corresponding limiting model with one fewer layer. The convergence is established in two complementary senses: (i) strong $L^{2}$-convergence over arbitrary finite time intervals, and (ii) upper semi-continuity of the global attractors describing the large-time asymptotic behavior.