Asymptotic Analysis of Singularly Perturbed Abstract Evolution Equations in Banach and Hilbert Spaces

Dialla KONATE

Makale detayları

Asymptotic Analysis of Singularly Perturbed Abstract Evolution Equations in Banach and Hilbert Spaces

Yazarlar:

Dialla KONATE

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2002 Vol.26 Issue 4, pp.355-374

Belge Tipi:

Makale

Yayın Tarihi:

3/2002

Belge Dili:

Türkçe

Document ID (Org No.):

2000748920

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

In the current paper, we are concerned with the study of abstract  linear evolution equations in Banach spaces in which the time  derivative term is multiplied by a small parameter, say e.   Such equations arise in the study of radiative transfer and neutron  transport in Nuclear Physics.  Following works by Krein (cf [9]) and  others, Mika (cf [12,13,14,15]) using either the Hilbert method or the  Compressed method has shown that the solution of the given singularly  perturbed equation may be approximated upto any prescibed order by a  sum of two asymptotic expansions that are the outer expansion that is  valid far away" from the Initial layer and the Inner expansion which  vanishes out of a certain neighborhood of the Initial layer.  Since  the terms of the Inner expansion are usually difficult to calculated,  these higher order asymptotic approximations  often remain formal.  The main objectives of the current paper are:    - to locate precisely the Initial layer (cf [7,8])    - to show that making use of the concept of corrector as set by Lions  (cf [11]) the outer expansion alone (at the exclusion of the inner  expansion) suffices to achieve an approximation upto any prescribed  order of precision.    Moreover, these results are reached under hypotheses that are weaker  than those usually considered in the literature.  The asymptotic  solutions are worked out either in the general situation of Banach  spaces or in the case of Hilbert spaces.

 

In the current paper, we are concerned with the study of abstract  linear evolution equations in Banach spaces in which the time  derivative term is multiplied by a small parameter, say e.   Such equations arise in the study of radiative transfer and neutron  transport in Nuclear Physics.  Following works by Krein (cf [9]) and  others, Mika (cf [12,13,14,15]) using either the Hilbert method or the  Compressed method has shown that the solution of the given singularly  perturbed equation may be approximated upto any prescibed order by a  sum of two asymptotic expansions that are the outer expansion that is  valid far away" from the Initial layer and the Inner expansion which  vanishes out of a certain neighborhood of the Initial layer.  Since  the terms of the Inner expansion are usually difficult to calculated,  these higher order asymptotic approximations  often remain formal.  The main objectives of the current paper are:    - to locate precisely the Initial layer (cf [7,8])    - to show that making use of the concept of corrector as set by Lions  (cf [11]) the outer expansion alone (at the exclusion of the inner  expansion) suffices to achieve an approximation upto any prescribed  order of precision.    Moreover, these results are reached under hypotheses that are weaker  than those usually considered in the literature.  The asymptotic  solutions are worked out either in the general situation of Banach  spaces or in the case of Hilbert spaces.

Makale detayları

Asymptotic Analysis of Singularly Perturbed Abstract Evolution Equations in Banach and Hilbert Spaces

Yazarlar:

Dialla KONATE

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2002 Vol.26 Issue 4, pp.355-374

Belge Tipi:

Makale

Yayın Tarihi:

3/2002

Belge Dili:

Türkçe

Document ID (Org No.):

2000748920

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Singular Perturbation

Asymptotic Expansion

Banach space

semigroup

evolution equation

Initial Layer

Corrector

radiative transfer

neutron transport.

Sayı

Makale detayları

Yazarlar: Dialla KONATE

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2002 Vol.26 Issue 4, pp.355-374

Belge Tipi: Makale

Yayın Tarihi: 3/2002

Belge Dili: Türkçe

Document ID (Org No.): 2000748920

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Dialla KONATE

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2002 Vol.26 Issue 4, pp.355-374

Belge Tipi:

Makale

Yayın Tarihi:

3/2002

Belge Dili:

Türkçe

Document ID (Org No.):

2000748920

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098