Positivity and stability for a system of transport equations with unbounded boundary perturbations

Abstract

This article concerns wellposedness, positivity and spectral properties of the solution of a system of transport equations with unbounded boundary perturbations. In particular we obtain that the rescaled solution converges to the unique steady-state solution as time approaches infinity on a weighted L^1-space.

Keywords

• System of transport equations
• C_0-semigroup
• irreducibility
• dominant eigenvalue
• asymptotic properties
• unbounded boundary perturbation