Some remarks on densely defined streaming operators. (English) Zbl 0824.47057
Summary: We show that the streaming operator in particle transport problems and in population dynamics is densely defined, even if the boundary conditions are not the standard nonreentry boundary conditions.
MSC:
| 47N60 | Applications of operator theory in chemistry and life sciences |
| 92D25 | Population dynamics (general) |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 47A05 | General (adjoints, conjugates, products, inverses, domains, ranges, etc.) |
| 47A55 | Perturbation theory of linear operators |
Keywords:
semigroups of operators; perturbation of resolvents; particle streaming; age-structured population; streaming operator; particle transport problems; population dynamics; nonreentry boundary conditionsReferences:
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| [2] | M. Mokhtar-Kharroubi, personal communication, (1993).; M. Mokhtar-Kharroubi, personal communication, (1993). |
| [3] | Greiner, G., Perturbing the boundary conditions of a generator, Houston J. Math, 13, 213-229 (1987) · Zbl 0639.47034 |
| [4] | Webb, G. F., Theory of Nonlinear Age Dependent Population Dynamics (1985), Marcel Dekker: Marcel Dekker New York · Zbl 0555.92014 |
| [5] | Belleni-Morante, A., A Concise Guide to Semigroups and Evolution Equations (1994), World Scientific: World Scientific Singapore · Zbl 0807.34074 |
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