The Asymptotic Behavior of the Solution to a Cauchy Problem Governed by a Transport Operator
Aref Jeribi, Khalid Latrach, Hatem Megdiche · Journal of Integral Equations and Applications · 2005
The purpose of this paper is to investigate some spectral properties of a time-dependent linear transport equation with diffusive boundary conditions arising in growing cell populations.After deriving the explicit expression of the strongly continuous semigroup {U K (t) : t ≥ 0} generated by the streaming operator, we establish the strict singularity of the operator BU K (s)B, s > 0, for a wide class of collision operators B. Making use of the Weis theorem, Theorem 4.1, this enables us to estimate the essential type of the transport semigroup from which the asymptotic behavior of the solution is derived.