Geodesic
Estimates of the stabilization rate as $t\to\infty$ of solutions of the~first mixed problem for a~quasilinear system of second-order parabolic equations
Sbornik. Mathematics, Tome 191 (2000) no. 2, pp. 235-273

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

A quasilinear system of parabolic equations with energy inequality is considered in a cylindrical domain $\{t>0\}\times\Omega$. In a broad class of unbounded domains $\Omega$ two geometric characteristics of a domain are identified which determine the rate of convergence to zero as $t\to\infty$ of the $L_2$-norm of a solution. Under additional assumptions on the coefficients of the quasilinear system estimates of the derivatives and uniform estimates of the solution are obtained; they are proved to be best possible in the order of convergence to zero in the case of one semilinear equation. 
@article{SM_2000_191_2_a3,
     author = {L. M. Kozhevnikova and F. Kh. Mukminov},
     title = {Estimates of the stabilization rate as $t\to\infty$ of solutions of the~first mixed problem for a~quasilinear system of second-order parabolic equations},
     journal = {Sbornik. Mathematics},
     pages = {235--273},
     publisher = {mathdoc},
     volume = {191},
     number = {2},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_2_a3/}
}
TY  - JOUR
AU  - L. M. Kozhevnikova
AU  - F. Kh. Mukminov
TI  - Estimates of the stabilization rate as $t\to\infty$ of solutions of the~first mixed problem for a~quasilinear system of second-order parabolic equations
JO  - Sbornik. Mathematics
PY  - 2000
SP  - 235
EP  - 273
VL  - 191
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2000_191_2_a3/
LA  - en
ID  - SM_2000_191_2_a3
ER  - 
%0 Journal Article
%A L. M. Kozhevnikova
%A F. Kh. Mukminov
%T Estimates of the stabilization rate as $t\to\infty$ of solutions of the~first mixed problem for a~quasilinear system of second-order parabolic equations
%J Sbornik. Mathematics
%D 2000
%P 235-273
%V 191
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2000_191_2_a3/
%G en
%F SM_2000_191_2_a3
L. M. Kozhevnikova; F. Kh. Mukminov. Estimates of the stabilization rate as $t\to\infty$ of solutions of the~first mixed problem for a~quasilinear system of second-order parabolic equations. Sbornik. Mathematics, Tome 191 (2000) no. 2, pp. 235-273. http://geodesic.mathdoc.fr/item/SM_2000_191_2_a3/