Geodesic
The first boundary-value problem for a~fractional diffusion-wave equation in a~non-cylindrical domain
Izvestiya. Mathematics , Tome 81 (2017) no. 6, pp. 1212-1233

Voir la notice de l'article provenant de la source Math-Net.Ru

We solve the first boundary-value problem in a non-cylindrical domain for a diffusion-wave equation with the Dzhrbashyan–Nersesyan operator of fractional differentiation with respect to the time variable. We prove an existence and uniqueness theorem for this problem, and construct a representation of the solution. We show that a sufficient condition for unique solubility is the condition of Hölder smoothness for the lateral boundary of the domain. The corresponding results for equations with Riemann–Liouville and Caputo derivatives are particular cases of results obtained here.
Keywords: first boundary-value problem, fractional derivative, Dzhrbashyan–Nersesyan operator
Mots-clés : diffusion-wave equation, non-cylindrical domain. 
@article{IM2_2017_81_6_a7,
     author = {A. V. Pskhu},
     title = {The first boundary-value problem for a~fractional diffusion-wave equation in a~non-cylindrical domain},
     journal = {Izvestiya. Mathematics },
     pages = {1212--1233},
     publisher = {mathdoc},
     volume = {81},
     number = {6},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2017_81_6_a7/}
}
TY  - JOUR
AU  - A. V. Pskhu
TI  - The first boundary-value problem for a~fractional diffusion-wave equation in a~non-cylindrical domain
JO  - Izvestiya. Mathematics 
PY  - 2017
SP  - 1212
EP  - 1233
VL  - 81
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2017_81_6_a7/
LA  - en
ID  - IM2_2017_81_6_a7
ER  - 
%0 Journal Article
%A A. V. Pskhu
%T The first boundary-value problem for a~fractional diffusion-wave equation in a~non-cylindrical domain
%J Izvestiya. Mathematics 
%D 2017
%P 1212-1233
%V 81
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2017_81_6_a7/
%G en
%F IM2_2017_81_6_a7
A. V. Pskhu. The first boundary-value problem for a~fractional diffusion-wave equation in a~non-cylindrical domain. Izvestiya. Mathematics , Tome 81 (2017) no. 6, pp. 1212-1233. http://geodesic.mathdoc.fr/item/IM2_2017_81_6_a7/