Evolution equations with a parameter and  application to transport-convection differential equations

Emile Franc Doungmo GOUFO

Makale detayları

Evolution equations with a parameter and application to transport-convection differential equations

Yazarlar:

Emile Franc Doungmo GOUFO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2017 Vol.41 Issue 3, pp.636-654

Belge Tipi:

Makale

Yayın Tarihi:

5/2017

Belge Dili:

Türkçe

Document ID (Org No.):

2000746049

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

We deeply investigate the well-posedness  of  models taking the form A0Dβtu(t)=Au(t),u(0)=f,000ADtβu(t)=Au(t),u(0)=f,00_0^AD^{\beta }_tu(t) = Au(t),\;\; u(0)= \,f,\;\;\;00 where A0Dβt0ADtβ_0^AD^{\beta }_t is a derivative with the fractional parameter ββ\beta and AAA is a closed densely defined operator in a Banach space. We show that, unlike other systems, solutions of our models are not governed by Mittag--Leffler functions and their variants. We extend and adapt Peano's idea to our models and establish conditions for existence and uniqueness of solutions. In particular, relations between the two-parameter solution operator, its resolvent, and its generator are provided; the issue of subordination and prolongation principles are addressed; and a way to approximate the generalized solution is presented. Finally, application to transport-convection differential equations is performed in the space of distributions with finite higher moments to show how their well-posedness can be addressed.

Makale detayları

Evolution equations with a parameter and application to transport-convection differential equations

Yazarlar: Emile Franc Doungmo GOUFO

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2017 Vol.41 Issue 3, pp.636-654

Belge Tipi: Makale

Yayın Tarihi: 5/2017

Belge Dili: Türkçe

Document ID (Org No.): 2000746049

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Emile Franc Doungmo GOUFO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2017 Vol.41 Issue 3, pp.636-654

Belge Tipi:

Makale

Yayın Tarihi:

5/2017

Belge Dili:

Türkçe

Document ID (Org No.):

2000746049

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098