Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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{\textendash}Dirichlet} problem for some class of doubly nonlinear parabolic equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {48--65},
     year = {1994},
     volume = {213},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a2/}
}
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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/