Electron. J. Diff. Equ.,
Vol. 2009(2009), No. 137, pp. 1-13.
Positivity and stability for a system of transport equations with
unbounded boundary perturbations
Ciro D'Apice, Brahim El habil, Abdelaziz Rhandi
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.
Submitted September 16, 2009. Published October 25, 2009.
Math Subject Classifications: 47D06, 46B42, 34D05, 34G10, 47A10, 47A55, 47B65.
Key Words: System of transport equations; C_0-semigroup;
irreducibility; dominant eigenvalue; asymptotic properties;
unbounded boundary perturbation.
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Ciro D'Apice
Dipartimento di Ingegneria dell'Informazione e Matematica
Applicata
Università degli Studi di Salerno
Via Ponte Don Melillo 84084 Fisciano (Sa), Italy
email: dapice@diima.unisa.it
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Brahim El habil
Department of Mathematics, Faculty of Science Semlalia
Cadi Ayyad University
B.P. 2390, 40000, Marrakesh, Morocco
email: b.elhabil@ucam.ac.ma
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Abdelaziz Rhandi
Dipartimento di Ingegneria dell'Informazione e Matematica Applicata
Università degli Studi di Salerno
Via Ponte Don Melillo 84084 Fisciano (Sa), Italy.
Department of Mathematics, Faculty of Science Semlalia
Cadi Ayyad University,
B.P. 2390, 40000, Marrakesh, Morocco
email: rhandi@diima.unisa.it
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