Geodesic
Existence and uniqueness theorems for solutions of parabolic equations with a~variable nonlinearity exponent
Sbornik. Mathematics, Tome 205 (2014) no. 3, pp. 307-318

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The paper is concerned with the solvability of the initial-boundary value problem for second-order parabolic equations with variable nonlinearity exponents. In the model case, this equation contains the $p$-Laplacian with a variable exponent $p(x,t)$. The problem is shown to be uniquely solvable, provided the exponent $p$ is bounded away from both $1$ and $\infty$ and is log-Hölder continuous, and its solution satisfies the energy equality. Bibliography: 18 titles.
Keywords: variable nonlinearity exponent, log-Hölder continuity.
Mots-clés : parabolic equation 
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     author = {Yu. A. Alkhutov and V. V. Zhikov},
     title = {Existence and uniqueness theorems for solutions of parabolic equations with a~variable nonlinearity exponent},
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Yu. A. Alkhutov; V. V. Zhikov. Existence and uniqueness theorems for solutions of parabolic equations with a~variable nonlinearity exponent. Sbornik. Mathematics, Tome 205 (2014) no. 3, pp. 307-318. http://geodesic.mathdoc.fr/item/SM_2014_205_3_a0/