Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Tome 200 (1992), pp. 110-117
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P. Z. Mkrtychian. On uniqueness of solution of the second initial-boundary value problem for non-Nеwtonian politropical filtration equation. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Tome 200 (1992), pp. 110-117. http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a10/
@article{ZNSL_1992_200_a10,
author = {P. Z. Mkrtychian},
title = {On uniqueness of solution of the second initial-boundary value problem for {non-N{\cyre}wtonian} politropical filtration equation},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {110--117},
year = {1992},
volume = {200},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a10/}
}
TY - JOUR
AU - P. Z. Mkrtychian
TI - On uniqueness of solution of the second initial-boundary value problem for non-Nеwtonian politropical filtration equation
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1992
SP - 110
EP - 117
VL - 200
UR - http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a10/
LA - ru
ID - ZNSL_1992_200_a10
ER -
%0 Journal Article
%A P. Z. Mkrtychian
%T On uniqueness of solution of the second initial-boundary value problem for non-Nеwtonian politropical filtration equation
%J Zapiski Nauchnykh Seminarov POMI
%D 1992
%P 110-117
%V 200
%U http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a10/
%G ru
%F ZNSL_1992_200_a10
The uniqueness of non-negative solution of the second initial-boundary value problem for the equation $$ u_t-\sum_{i=1}^n\frac{\partial}{\partial x_i}|u|^l|u_{x_i}|^{m-2}u_{x_i}=0,\quad l\geqslant1,\ m\geqslant2,\ n\geqslant2, $$ in the class of functions $\{u: u\in L^\infty(Q_T)\cap C([0,T];L^2(\Omega)), (u^{l/m+1})_{x_i}\in L^m(Q_T)\}$ is established.
