Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces

F. Kh. Mukminov

Sbornik. Mathematics, Tome 208 (2017) no. 8, pp. 1187-1206

Résumé

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.

Détail

Keywords: renormalized solution, variable nonlinearity, uniqueness of solution, $N$-function.
Mots-clés : anisotropic parabolic equation

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