Expansion of Solution in Terms of Generalized Eigenvectors for a Rectilinear Transport Equation
Salma Charfi, Abdelkader Intissar, Aref Jeribi · Transport Theory and Statistical Physics · 2009
This article considers a time-dependent rectilinear transport equation that was first studied in B. Montagnini and V. Pierpaoli (Transport Theory and Statistical Physics 1(1) (1971) 59–75). The associated transport operator is the infinitesimal generator of a C 0-semigroup, its spectrum is discrete, and there are only finitely many eigenvalues in each vertical strip. We show that the C 0-semigroup can be expanded by its generalized eigenvectors, and we assert its differentiability.