Geodesic
Uniqueness of the renormalized solution of an elliptic-parabolic problem in~anisotropic Sobolev-Orlicz spaces
Sbornik. Mathematics, Tome 208 (2017) no. 8, pp. 1187-1206

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We consider the first mixed problem for a class of anisotropic elliptic-parabolic equations with double variable nonlinearities in a cylindrical domain $(0,T)\times\Omega$. The domain $\Omega\subset\mathbb{R}^n$ can be unbounded. The uniqueness of the renormalized solution is proved using Kruzhkov's method of doubling the variable $t$. The same result is established for an equation with non-power law nonlinearities. Bibliography: 24 titles.
Keywords: renormalized solution, variable nonlinearity, uniqueness of solution, $N$-function.
Mots-clés : anisotropic parabolic equation 
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     author = {F. Kh. Mukminov},
     title = {Uniqueness of the renormalized solution of an elliptic-parabolic problem in~anisotropic {Sobolev-Orlicz} spaces},
     journal = {Sbornik. Mathematics},
     pages = {1187--1206},
     publisher = {mathdoc},
     volume = {208},
     number = {8},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_8_a4/}
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F. Kh. Mukminov. Uniqueness of the renormalized solution of an elliptic-parabolic problem in~anisotropic Sobolev-Orlicz spaces. Sbornik. Mathematics, Tome 208 (2017) no. 8, pp. 1187-1206. http://geodesic.mathdoc.fr/item/SM_2017_208_8_a4/