Theory of strongly continuous semigroups of continuous linear operators applied to a transport-diffusion equation

Abstract

In this work we apply the theory of semigroups of continuous linear operators to prove the existence and uniqueness of the solution for a certain transport-diffusion equation, in particular those that are strongly continuous, since they are generated by a linear operator usually denoted by A and commonly called the infinitesimal generator of the semigroup. This operator is of great importance since it is usually the operator related to an equation or system of differential equations, that is, we relate the transport-diffusion equation with a linear differential operator that generates a strongly continuous semigroup, and thus apply certain known results in the area of the semigroups and that will allow us to prove the existence and uniqueness of the solution for our equation, in contrast with the classic methods known.