Existence and uniqueness of a weak solution to the initial mixt boundary value problem for quasilinear
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 67-88
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We prove the existence and the uniqueness of a weak solution to the mixed boundary problem for the elliptic-parabolic equation
\begin{gather*}
\partial_tb(u)-\operatorname{div}\{|\sigma(u)|^{m-2}\sigma(u)\}=f(x,t),
\\
\delta(u):=\nabla u+k(b(u))\vec e, \qquad |\vec e|=1, \enskip m>1,
\end{gather*}
with a monotone nondecreasing continuous function $b$. Such equations arise in the theory of non-Newtonian filtration as well as in the mathematical glaciology.
@article{ZNSL_1999_259_a3,
author = {A. V. Ivanov and J.-F. Rodrigues},
title = {Existence and uniqueness of a weak solution to the initial mixt boundary value problem for quasilinear},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {67--88},
publisher = {mathdoc},
volume = {259},
year = {1999},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a3/}
}
TY - JOUR AU - A. V. Ivanov AU - J.-F. Rodrigues TI - Existence and uniqueness of a weak solution to the initial mixt boundary value problem for quasilinear JO - Zapiski Nauchnykh Seminarov POMI PY - 1999 SP - 67 EP - 88 VL - 259 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a3/ LA - en ID - ZNSL_1999_259_a3 ER -
%0 Journal Article %A A. V. Ivanov %A J.-F. Rodrigues %T Existence and uniqueness of a weak solution to the initial mixt boundary value problem for quasilinear %J Zapiski Nauchnykh Seminarov POMI %D 1999 %P 67-88 %V 259 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a3/ %G en %F ZNSL_1999_259_a3
A. V. Ivanov; J.-F. Rodrigues. Existence and uniqueness of a weak solution to the initial mixt boundary value problem for quasilinear. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 67-88. http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a3/