Time-dependent kinetic equations with collision terms relatively bounded with respect to the collision frequency

Transport Theory and Statistical Physics

Volumn 30, Issue 1, 2001, Pages 63-90

  Van Der Mee, Cornelis ^a  

^a UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035601593     PISSN: 00411450     EISSN: None     Source Type: Journal    
DOI: 10.1081/TT-100104455     Document Type: Article

References (32)

1. L. Arlotti and G. Frosali, Runaway particles for a Boltzmann-like transport equation, Math. Models Meth. Appl. Sci. 2, 203-221 (1992).
2. C. Bardos, Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; Thèorèmes d'approximation; Application à l'équation de transport, Ann. Scient. École Normale Supérieure, Série 4, 3, 185-233 (1970).
3. R. Beals and V. Protopopescu, Abstract time dependent transport equations, J. Math. Anal. Appl. 121, 370-405 (1987).
4. 0-Semi-groupe (I), Preprint.
5. K.M. Case and P.F. Zweifel, Linear Transport Theory, Addison-Wesley, Read, MA, 1967.
6. C. Cercignani, The Boltzmann Equation and its Applications, Appl. Math. Sciences 67, Springer, Berlin, 1988.
7. S. Chandrasekhar, Radiative Transfer, Oxford Univ. Press, London, 1950; also: Dover Publ., New York, 1960.
8. p pour des espaces de fonctions de la neutronique, Comptes Rendus Acad. Sci. Paris, Série 1, 299, 831-834 (1984).
9. M. Cessenat, Théorèmes de trace pour des espaces de fonctions de la neutronique, Comptes Rendus Acad. Sci. Paris, Série 1, 300, 89-92 (1985).
10. C. Chicone and Yu. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, Math. Surveys and Monographs 70, Amer. Math. Soc., Providence, R.I., 1999.
11. F. Chvála, Weak solutions of the linear Boltzmann equation with very soft interactions, J. Math. Anal. Appl. 191, 360-379 (1995).
12. F. Chvála, T. Gustafsson and R. Pettersson, On solutions to the linear Boltzmann equation with external electromagnetic force, SIAM J. Math. Anal. 24, 583-602 (1993).
13. J. Diestel and J.J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, 1977.
14. N. Dunford and J.T. Schwartz, Linear Operators, Part I, Wiley-Interscience, New York and London, 1958.
15. G. Frosali, C.V.M. van der Mee and S.L. Paveri-Fontana, Conditions for runaway phenomena in the kinetic theory of particle swarms, J. Math. Phys. 30, 1177-1186 (1989).
16. W. Greenberg, C. van der Mee, and V. Protopopescu, Boundary Value Problems in Abstract Kinetic Theory, Birkhäuser OT 23, Basel-Boston-Stuttgart, 1987.
17. H.G. Kaper, C.G. Lekkerkerker, and J. Hejtmanek, Spectral Methods in Linear Transport Theory, Birkhäuser OT 5, Basel-Boston-Stuttgart, 1982.
18. A. Majorana, Space homogeneous solutions of the Boltzmann equation describing electron-phonon interactions in semiconductors, Transport Theory Statist. Phys. 20, 261-279 (1991).
19. A. Majorana and C. Milazzo, Space homogeneous solution of the linear semiconductor Boltzmann equation, Preprint (2000).
20. C.V.M. van der Mee, A transport equation modelling cell growth. In: P. Tautu (Ed.), Stochastic Modelling in Biology. Relevant Mathematical Concepts and Recent Applications, World Scientific, Singapore, 1990, pp. 381-398.
21. C.V.M. van der Mee, Trace theorems and kinetic equations for non divergence free external forces, Applicable Analysis 41, 89-110 (1991).
22. R. Nagel, Semigroup methods for non-autonomous Cauchy problems, Tübinger Berichte zur Funktionalanalysis, Heft 2, Jahrgang 92/93, Tübingen, 1993, pp. 103-118.
23. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983.
24. R. Pettersson, On solutions to the linear Boltzmann equation with general boundary conditions and infinite-range forces, J. Statist. Phys. 59, no. 1-2, 403-440 (1990).
25. F. Poupaud, Critères d'existence de solutions stationnaires homogènes en théorie cinétique des semi-conducteurs. Application à l'approximation fluide à champ fort, C.R. Acad. Sci. Paris, Série I, 308, 381-386 (1989).
26. F. Poupaud, Runaway phenomena and fluid approximation under high fields in semiconductor kinetic theory, Z. Angew. Math. Mech. 72, 359-372 (1992).
27. R.T. Rau, Hyperbolic evolution groups and dichotomic evolution families, J. Dynam. Differential Equations 6, 335-350 (1994).
28. M. Rotenberg, Transport theory for growing cell populations, J. Theor. Biol. 103, 181-199 (1983).
29. V.V. Sobolev, Light Scattering in Planetary Atmospheres, Pergamon Press, Oxford, 1975; also: Nauka, Moscow, 1972 [Russian].
30. S. Ukai, Solutions of the Boltzmann equation. Patterns and waves. Qualitative analysis of nonlinear differential equations, Stud. Math. Appl. 18, 37-96 (1986).
31. J. Voigt, Functional-analytic treatment of the initial-boundary value problem for collisionless gases, Habilitationsschrift, Ludwig Maximilians Universität München, 1980.
32. J. Voigt, Absorption Semigroups, J. Operator Theory 20, 117-131 (1988).