Dissipation-minimization conjecture for periodic porous-medium solutions

Let $s^*(\xi^*)$ be a periodic prescribed forcing with period $L$, and let $u_s^*$ and $u_f^*$ denote the corresponding nondimensional solid and fluid velocities. For parameters $(V,A_s,A_f)$, define the dissipation by

$$R=\int_0^L K^*(u_s^*-u_f^*)^2\,\mathrm{d}\xi.$$

Dissipation-minimization conjecture. The parameters $(V,A_s,A_f)$ are chosen in such a way that the dissipation $R$ is minimal. The claim concerns the selection of parameters for a periodic solution of the nondimensional first-order ODE, but the source does not provide an analytical derivation or a precise admissible class over which the minimum is taken.