Existence and uniqueness of positive solutions to a linear transport equation in a metric space Original Research Article

The linear functional equation ∂tz = L(z) − rz is considered. The linear operator L acts on a linear metric space of real functions z depending on t and on a parameter ω belonging to a subset of View the MathML sourcem. The existence and uniqueness to a nonnegative solution of the initial value problem is shown. An application to a kinetic equation is performed.