Geodesic
Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour
Nanosistemy: fizika, himiâ, matematika, Tome 8 (2017) no. 1, pp. 5-12.

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

In this paper, we study the properties of self-similar solutions of a cross-diffusion parabolic system. In particular, we find the Zeldovich–Barenblatt type solution to the cross diffusive system. The asymptotic behavior of self-similar solutions are analyzed for both the slow and fast diffusive regimes. It is shown that coefficients of the main term of the asymptotic of solution satisfy some system of nonlinear algebraic equations.
Keywords: cross-diffusive system, finite speed, asymptotic behavior, numerical analysis.
Mots-clés : non-divergence form, perturbation, global solutions 
@article{NANO_2017_8_1_a0,
     author = {M. M. Aripov and A. S. Matyakubov},
     title = {Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {5--12},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2017_8_1_a0/}
}
TY  - JOUR
AU  - M. M. Aripov
AU  - A. S. Matyakubov
TI  - Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour
JO  - Nanosistemy: fizika, himiâ, matematika
PY  - 2017
SP  - 5
EP  - 12
VL  - 8
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/NANO_2017_8_1_a0/
LA  - en
ID  - NANO_2017_8_1_a0
ER  - 
%0 Journal Article
%A M. M. Aripov
%A A. S. Matyakubov
%T Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour
%J Nanosistemy: fizika, himiâ, matematika
%D 2017
%P 5-12
%V 8
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/NANO_2017_8_1_a0/
%G en
%F NANO_2017_8_1_a0
M. M. Aripov; A. S. Matyakubov. Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour. Nanosistemy: fizika, himiâ, matematika, Tome 8 (2017) no. 1, pp. 5-12. http://geodesic.mathdoc.fr/item/NANO_2017_8_1_a0/