Existence and uniqueness of regular solution of Cauchy--Dirichlet problem for some class of doubly nonlinear parabolic equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 48-65
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The class of equations of the type
\begin{equation}
\partial u/\partial t-\operatorname{div}\vec a(u,\nabla u)=f,
\tag{1}
\end{equation}
such that
\begin{equation}
\begin{gathered}
\vec a(u,p)\cdot p\ge\nu_0|u|^l|p|^m-\Phi_0(u),\\
|\vec a(u,p)|\le\mu_1|u|^l|p|^{m-1}+\Phi_1(u)
\end{gathered}
\tag{2}
\end{equation}
with some $m\in(1,2)$, $l\ge0$ and $\Phi_i(u)\ge0$ is studied. Similar equations arise in the study of turbulent filtration of gas or a liquid through porous media. Existence and uniqueness in some class of Hölder continuous generalized solutions of Cauchy–Dirichlet problem for equations of the type (1), (2) is proved. Bibliography: 9 titles.
@article{ZNSL_1994_213_a2,
author = {A. V. Ivanov and P. Z. Mkrtychian and W. J\"ager},
title = {Existence and uniqueness of regular solution of {Cauchy--Dirichlet} problem for some class of doubly nonlinear parabolic equations},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {48--65},
publisher = {mathdoc},
volume = {213},
year = {1994},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a2/}
}
TY - JOUR AU - A. V. Ivanov AU - P. Z. Mkrtychian AU - W. Jäger TI - Existence and uniqueness of regular solution of Cauchy--Dirichlet problem for some class of doubly nonlinear parabolic equations JO - Zapiski Nauchnykh Seminarov POMI PY - 1994 SP - 48 EP - 65 VL - 213 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a2/ LA - ru ID - ZNSL_1994_213_a2 ER -
%0 Journal Article %A A. V. Ivanov %A P. Z. Mkrtychian %A W. Jäger %T Existence and uniqueness of regular solution of Cauchy--Dirichlet problem for some class of doubly nonlinear parabolic equations %J Zapiski Nauchnykh Seminarov POMI %D 1994 %P 48-65 %V 213 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a2/ %G ru %F ZNSL_1994_213_a2
A. V. Ivanov; P. Z. Mkrtychian; W. Jäger. Existence and uniqueness of regular solution of Cauchy--Dirichlet problem for some class of doubly nonlinear parabolic equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 48-65. http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a2/