On the approximation of the leading eigenelements for a class of transport operators

References

• Asadzadeh , M. 1989 . Lp and eigenvalue error estimates for the discrete ordinate method for two–dimensional neutron transport . SIAM J. Numer. Anal. , 26 : 66 – 87 .
   Web of Science ®Google Scholar
• Bardos , C. 1970 . Boundary value problems for first order partial differential equations with real coefficients; approximation theorems, application to the transport equation . Ann. Scient. Ecole Normale Sup. , t. 3 : 185 – 233 . série 4
   Google Scholar
• Caselles , V. 1987 . On the peripheral spectrum of positive operators . Israel J. Math. , 58 : 144 – 160 .
   Web of Science ®Google Scholar
• Cesenat , M. 1984 . Théorèmes de trace Lp pour des espaces de fonctions de la neutronique . C. R. Acad. Sc. Paris , 299 : 831 – 834 . série I
   Google Scholar
• Cessenat , M. 1985 . Théorèmes de trace pour des espaces de fonctions de la neutronique . C. R. Acad. Sc. Paris , 300 : 89 – 92 . série I
   PubMed Web of Science ®Google Scholar
• Chatelin , F. 1983 . Spectral approximation of linear operators . Comp. Sci. and Appl. Math. Ac. Press ,
   Google Scholar
• Dautray , R. and Lions , J. L. 1988 . Analyse mathématique et calcul numérique . Méthodes intégrates et numériques , vol. 6 Masson
   Google Scholar
• De Pagter , B. 1986 . Irreducible compact operators . Math. Zeits. , 192 : 149 – 153 .
   Web of Science ®Google Scholar
• Gilbarg , D. and Trudinger , N. S. 1983 . Elliptic partial differential operators , Springer-Verlag .
   Google Scholar
• Greenberg , W. 1987 . Boundary value problems in abstract kinetic theory , Birkhäuser Verlag .
   Google Scholar
• Kaper , H. G. , Lekkerkerker , C. and Hejtmanek , G. 1982 . Spectral methods in linear transport theory , Birkhäuser Verlag .
   Google Scholar
• Kato , T. 1982 . Superconvexity of the spectral radius and convexity of the spectral bound and the type . Math. Zeits. , : 263 – 273 .
   Web of Science ®Google Scholar
• Kato , T. 1980 . Perturbation theory for linear operators , Springer Verlag .
   Google Scholar
• Kingman , J. F. C. 1961 . A convexity property of positive matrices . Quart. J. Math. Oxford , 12 ( 2 ) : 283 – 284 .
   Web of Science ®Google Scholar
• Larsen , E. W. 1979 . The spectrum of the multigroup neutron transport operator for bounded spatial domains . J. Math. Phys. , 20 : 1776 – 1782 .
   Web of Science ®Google Scholar
• Marek , I. 1971 . Approximation of the principal eigenelements in K-positive nonselfadjoint eigenvalue problem. . Math. Systems Theory , 5 : 204 – 215 .
   Google Scholar
• Marek , I. 1970 . Frobenius theory of positive operators. Comparison theorems and applications . SIAM J. Appl. Math. , 19 : 607 – 628 .
   Web of Science ®Google Scholar
• Mokhtar-Kharroubi , M. 1983 . Propriétés spectrales de l'opérateur de transport dans le cas anisotrope , Vol. VI , Université de Paris . Thèse de 3ème cycle
   Google Scholar
• Mokhtar-Kharroubi , M. 1986 . La compacité dans la théorie du transport des neutrons . C. R. Acad. Sc. Paris , t. 303 ( 13 ) : 617 – 619 .
   Google Scholar
• Mokhtar-Kharroubi , M. 1992 . The time asymptotic behaviour and the compactness in neutron transport theory . Eur. J. Mech. B. Fluids , 11 ( 1 ) : 39 – 68 .
   Web of Science ®Google Scholar
• Mokhtar-Kharroubi , M. 1987 . Some spectral properties of the neutron transport operator in bounded geometries . TTSP , t. 16 ( 7 ) : 935 – 958 .
   Google Scholar
• Mokhtar-Kharroubi , M. 1991 . W1,p regularity in transport theory . Mathematical models and methods in applied sciences , vol. 1 ( 4 ) : 477 – 499 .
   Google Scholar
• Mokhtar-Kharroubi , M. 1990 . Quelques applications de la positivité en théorie du transport . Annal. Fac. Sci. Toulouse , vol. XI ( 1 ) : 75 – 99 .
   Google Scholar
• Mokhtar-Kharroubi , M. On the approximation of a class of transport equations To appear in TTSP.
   Google Scholar
• Nagel , R. 1986 . “ One-parameter semigroups of positive operators ” . In Lecture Notes in Mathematics , Springer Verlag . n°1184
   Google Scholar
• Schaefer , H. H. 1974 . Banach lattices and positive operators , Springer Verlag .
   Google Scholar
• Vidav , I. 1968 . Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator . J. Math. and Appl. , 22 : 144 – 155 .
   Web of Science ®Google Scholar
• Voigt , J. 1980 . Functional analytic treatment of the initial boundary value problem for collisionless gases , Munchen : Habilitations-schrift .
   Google Scholar
• Voigt , J. 1984 . Positivity in time dependent transport theory . Acta Applicandae Mathematicae , 2 : 311 – 331 .
   Web of Science ®Google Scholar
• Wing , G. M. 1962 . An introduction to transport theory , New-York : Wiley .
   Google Scholar
• Arandiga , F. 1992 . Approximacion de operadores Y continuidad del radio espectral , Thesis in Spanish Universitat de Valencia .
   Google Scholar
• Arandiga , F. and Caselles , V. Work in preparation.
   Google Scholar