  In the present paper, we study the existence, uniqueness and behaviour in
time of the solutions to the Darcy-B\'enard problem for an
extended-quasi-thermal-incompressible fluid-saturated porous medium uniformly
heated from below. Unlike the classical problem, where the compressibility
factor of the fluid vanishes, in this paper we allow the fluid to be slightly
compressible and we address the well-posedness analysis for the full nonlinear
initial boundary value problem for the perturbed system of governing equations
modelling the convection in porous media phenomenon.
