Some Mathematical Aspects of f(R)-Gravity with Torsion: Cauchy Problem and Junction Conditions

We discuss the Cauchy problem and the junction conditions within the framework of $f(R)$-gravity with torsion. We derive sufficient conditions to ensure the well-posedness of the initial value problem, as well as general conditions to join together on a given hypersurface two different solutions of the field equations. The stated results can be useful to distinguish viable from nonviable $f(R)$-models with torsion.