Quintessence models of Dark Energy with non-minimal coupling

We explore quintessence models of dark energy which exhibit non-minimal coupling between the dark matter and the dark energy components of the cosmic fluid. The kind of coupling chosen is inspired in scalar-tensor theories of gravity. We impose a suitable dynamics of the expansion allowing to derive exact Friedmann-Robertson-Walker solutions once the coupling function is given as input. Coupling functions that lead to self-interaction potentials of the single and double exponential types are the target of the present investigation. The stability and existence of the solutions is discussed in some detail. The models are tested against the observational evidence.