This paper deals with spectral properties of a class of neutron transport equations involving partly elastic collision operators introduced by Larsen and Zweifel [J. Math. Phys.15, 19871997 (1974)]. In particular, estimates of the essential type of associated semigroups are given.

1.
S.
Brendle
, “
On the asymptotic behaviour of perturbed strongly continuous semigroups
,”
Math. Nachr.
226
,
35
47
(
2001
).
2.
H.
Brezis
,
Analyse Fonctionnelle, Théorie et Application
(
Masson
,
Paris
,
1983
).
3.
M.
Borysiewicz
, and
J.
Mika
, “
Time behavior of thermal neutrons in moderating media
,”
J. Math. Anal. Appl.
26
,
461
478
(
1969
).
4.
G.
Greiner
, “
Spectral properties and asymptotic behavior of the linear transport equations
,”
Math. Z.
85
,
167
177
(
1984
).
5.
K.
Jörgens
, “
An asymptotic expansion in the theory of neutron transport
,”
Commun. Pure Appl. Math.
11
,
219
242
(
1958
).
6.
M.
Krasnoselskii
,
Integral Operators in Spaces of Summable Functions
(
Nordhoff
,
Leyden
,
1976
).
7.
E. W.
Larsen
, and
P. F.
Zweifel
, “
Spectrum of the linear transport operator
,”
J. Math. Phys.
15
,
1987
1997
(
1974
).
8.
B.
Lods
, “
On linear kinetic equations involving unbounded cross-sections
,”
Math. Methods Appl. Sci.
27
,
1049
1075
(
2004
).
9.
A.
Majorana
, “
Space homogeneous solutions of the Boltzmann equation describing electron-phonon interaction in semiconductors
,”
Transp. Theory Stat. Phys.
20
,
261
279
(
1991
).
10.
M.
Mokhtar-Kharroubi
,
Mathematical Topics in Neutron Transport Theory, New Aspects
,
Series on Advances in Mathematics for Applied Sciences
Vol.
46
, (
World Scientific
,
Singapore
,
1997
).
11.
M.
Mokhtar-Kharroubi
, “
Optimal spectral theory of neutron transport models
,”
J. Funct. Anal.
226
,
21
47
(
2005
).
12.
R.
Nagel
, and
J.
Poland
, “
The critical spectrum of a strongly continuous semigroup
,”
Adv. Math.
152
,
120
133
(
2000
).
13.
M.
Sbihi
, Ph.D. thesis,
Université de Franche-Comté
,
2005
.
14.
M.
Sbihi
, “
A resolvant approach to the stability of essential and critical spectra of perturbed C0-semigroups on Hilbert spaces with applications to transport theory
,”
J. Evol. Equ.
(to be published); available at: http://www.springerlink.comcontent1424–3202?sortorder=asc&Content+Status=Accepted
15.
G.
Schlüchtermann
, “
On weakly-compact operators
,”
Math. Ann.
292
,
263
266
(
1992
).
16.
P.
Takac
, “
A spectral mapping theorem for the exponential function in linear transport theory
,”
Transp. Theory Stat. Phys.
14
,
655
667
(
1985
).
17.
I.
Vidav
, “
Spectra of perturbed semigroups with applications to transport theory
,”
J. Math. Anal. Appl.
30
,
264
279
(
1970
).
18.
J.
Voigt
, “
A perturbation theorem for the essential spectral radius of strongly continuous semigroups
,”
Monatsh. Math.
90
,
153
161
(
1980
).
19.
J.
Voigt
, “
Positivity in time-dependent linear transport theory
,”
Acta Appl. Math.
2
,
311
331
(
1984
).
20.
J.
Voigt
, “
Spectral properties of the neutron transport equation
,”
J. Math. Anal. Appl.
106
,
140
153
(
1985
).
21.
L.
Weis
, “
A generalization of the Vidav-Jorgens perturbation theorem for semigroup and its application to transport theory
,”
J. Math. Anal. Appl.
129
,
6
23
(
1988
).
22.
L.
Weis
, “
The stability of positive semigroups on Lp spaces
,”
Proc. Am. Math. Soc.
123
,
3089
3094
(
1995
).
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