An integrated semigroup approach for age structured equations with diffusion and non-homogeneous boundary conditions

In this work, we consider a linear age-structured problem with diffusion and non-homogeneous boundary conditions both for the age space variables. We handle by re-writing it as non-densely defined abstract Cauchy problem. To that aim develop new result on closedness of commutative sum two operators using theory integrated semigroups. As an application result, are able to associate suitable semigroup some spatial equipped conditions. This is characterized description its infinitesimal generator. Further applications our also given almost sectorial operators, which derive results.