Stabilization estimates for the Brinkman–Forchheimer–Kelvin–Voigt equation backward in time

Abstract

The final value value problem for the Brinkman–Forchheimer–Kelvin–Voigt equations is analysed for quadratic and cubic types of Forchheimer nonlinearity. The main term in the Forchheimer equations is allowed to be fully anisotropic. It is shown that the solution depends continuously on the final data provided the solution satisfies an a priori bound in $$L^3.$$ L 3 . The technique employed avoids the use of a specialist method for an improperly posed problem such as logarithmic convexity.