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Original Articles

On The Spectrum of Absorption Operators With Maxwell Boundary Conditions Arising in Population Dynamics and Transport Theory. A Unified Treatment

Pages 1-37 | Received 16 Feb 2004, Accepted 24 Jul 2005, Published online: 17 Sep 2008

References

  • Angelescu , N. , Marinescu , N. and Protopopescu , V. 1976 . On the spectrum of the linear transport operator with generalized boundary conditions . Lett. Math. Phys. , 1 : 141 – 146 .
  • Agoshkov , V. 1998 . Boundary value problems for transport equations , Boston : Birkhäuser .
  • Beals , R. and Protopopescu , V. 1987 . Abstract time-dependent transport equations . J. Math. Anal. Appl. , 121 : 370 – 405 .
  • Belleni-Morante , A. 1970 . Neutron transport in a uniform slab with generalized boundary conditions . J. Appl. Phys. , 5 : 1553 – 1558 .
  • Borgioli , G. and Frosali , G. 1986 . Criticality transport problems for spherical systems with specular type boundary conditions . Transp. Theory Stat. Phys. , 15 : 937 – 958 .
  • Boulanouar , M. 2001 . Study of the streaming operator with general Maxwell's boundary conditions . J. Dynam. Control Systems , 7 : 299 – 326 .
  • Boulanouar , M. and Emamirad , E. 2000 . The asymptotic behaviour of a transport equation in cell population dynamics with a null maturation velocity . J. Math. Anal. Appl. , 243 : 47 – 63 .
  • Corciovei , A. and Protopopescu , V. 1976 . On the spectrum of the linear transport operator with diffuse reflections . Rev. Roum. Phys. , 21 : 713 – 719 .
  • Jeribi , A. 2003 . Time asymptotic behaviour for unbounded linear operator arising growing cell populations . Nonlinear Anal. Real World Appl. , 4 : 667 – 688 .
  • Latrach , K. , Lods , B. and Mokhatr-Kharroubi , M. 2008 . Weak spectral mapping theorems for C0–groups and application to transport equations in slab geometry . J. Math. Anal. Appl. , 342 : 1038 – 1051 .
  • Latrach , K. and Mokhtar-Kharroubi , M. 1997 . On an unbounded linear operator arising in the theory of growing cell population . J. Math. Anal. Appl. , 211 : 273 – 294 .
  • Lebowitz , J. L. and Rubinow , S. I. 1974 . A theory for the age and generation time distribution of a microbial population . J. Math. Biol. , 1 : 17 – 36 .
  • Lods , B. 2002 . A generation theorem for kinetic equations with non-contractive boundary operators . C. R. Acad. Sci. Paris , 335 ( S'erie I ) : 655 – 660 .
  • Lods , B. and Mokhtar-Kharroubi , M. 2002 . On the theory of a growing cell population with zero minimum cycle length . J. Math. Anal. Appl. , 266 : 70 – 99 .
  • Mokhtar-Kharroubi , M. 2006 . Spectral properties of a class of positive semigroups on Banach lattices and streaming operators . Positivity , 10 : 231 – 249 .
  • Mokhtar-Kharroubi , M. 2002b . On the essential spectrum of transport operators in L1 spaces . Prep. Math. de Besanşon , : 27
  • Rotenberg , M. 1983 . Transport theory for growing cell populations . J. Theor. Biol. , 103 : 181 – 199 .
  • Sahni , D. C. , Garis , N. S. and Sjörstrand , N. G. 1995 . Spectrum of one-speed neutron transport operator with reflective boundary conditions in slab geometry . Transp. Theory Stat. Phys. , 24 : 629 – 656 .
  • Sahni , D. C. and Sjörstrand , N. G. 1998 . Time eigenvalues for one-speed neutrons in reflected spheres . Transp. Theory Stat. Phys. , 27 : 499 – 522 .
  • Schechter , M. 1971 . Spectra of Partial Differential Operators , Amsterdam : North Holland .
  • Song , D. and Greenberg , W. 2001 . Spectral properties of transport equations for slab geometry in L1 with reentry boundary conditions . Transp. Theory Stat. Phys. , 30 : 325 – 355 .
  • Totaro , S. and Belleni-Morante , A. 1995 . The free streaming operator: A mathematical model for diffusive multiplying boundary conditions . Math. Methods Appl. Sci. , 18 : 1165 – 1180 .
  • Ukai , S. 1986 . Solutions of the Boltzmann equation. Patterns and waves . Stud. Math. Appl. , 18 : 37 – 96 .
  • Van der Mee , C. , Greenberg , W. and Protopopescu , V. 1987 . Boundary value problems in abstract kinetic theory , Basel : Birkhauser Verlag .
  • Vidav , I. 1970 . Spectra of perturbed semigroup with applications to transport theory . J. Math. Anal. Appl. , 30 : 264 – 279 .
  • Voigt , J. 1980 . A perturbation theorem for the essential spectral radius of strongly continuous semigroups . Monatsh. Math. , 90 : 153 – 161 .
  • Wang , W. and Yuan , R. 1999 . On the spectrum of the linear transport operator in a slab geometry with generalized periodic boundary conditions . Transp. Theory Stat. Phys. , 28 : 181 – 189 .
  • Webb , G. F. 1986 . A model of proliferating cell population with inherited cycle length . J. Math. Biol. , 23 : 269 – 282 .
  • Webb , G. F. 1987 . Dynamics of structured populations with inherited properties . Comput. Math. Appl. , 13 : 749 – 757 .
  • Zhu , Y. M. and Xiang , Y. A. 1990 . On the spectrum of the transport operator for a bounded convex body . Acta Math. Sci. , 10 : 402 – 411 . [in Chinese]
  • Xianwen , Z. and Benzhong , L. 1997 . The spectrum of a one-velocity transport operator with integral boundary conditions of Maxwell-type . Transp. Theory Stat. Phys. , 26 : 85 – 102 .
  • Xianwen , Z. 1999 . Spectral properties of a streaming operator with diffuse reflection boundary conditions . J. Math. Anal. Appl. , 238 : 20 – 43 .

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