  The trend to equilibrium for reaction-diffusion systems coming out of
chemistry is investigated, in the case when reaction processes might happen
only on some open subsets of the domain. A special case has been studied
recently in [Desvillettes, L., \\& Phung, K. D. (2022). Journal of Differential
Equations, 338, 227-255] using log convexity technique from controllability
theory, which in turn requires some amount of regularity for the solutions, and
is difficult to generalise to more general systems. In this paper, we prove the
convergence to equilibrium directly using vector-valued functional
inequalities. One major advantage of our approach is that it allows to deal
with nonlinearities of arbitrary orders, for which only global renormalised
solutions are known to globally exist. For a specific situation where solutions
are known to be bounded, we also prove the convergence to equilibrium when the
diffusion as well as the reaction rates are degenerate. For this situation, we
also treat the case of reactions happening in a set of strictly positive
measure which may have an empty interior.
