Existence of a renormalized solution to an anisotropic parabolic problem with

F. Kh. Mukminov

Sbornik. Mathematics, Tome 209 (2018) no. 5, pp. 714-738

Résumé

The first boundary value problem is considered for a certain class of anisotropic parabolic equations with variable nonlinearity exponents in a cylindrical domain $( 0,T)\times\Omega$, where $\Omega$ is a bounded domain. The parabolic term in the equation has the form $(\beta(x,u))_t$ and is determined by the function $\beta(x,r)\in L_1(\Omega)$, where $r\in \mathbb R$, which only satisfies the Carathéodory condition and is increasing in $r$. The existence of a weak and a renormalized solution is proved. Bibliography: 26 titles.

Détail

Keywords: renormalized solution, variable nonlinearity exponents
Mots-clés : anisotropic parabolic equation, existence of a solution.

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