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This article is cited in 27 scientific papers (total in 27 papers)
Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent
Yu. A. Alkhutov, V. V. Zhikov Vladimir State University
Abstract:
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:
parabolic equation, variable nonlinearity exponent, log-Hölder continuity.
Received: 20.09.2012 and 15.01.2014
Citation:
Yu. A. Alkhutov, V. V. Zhikov, “Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent”, Mat. Sb., 205:3 (2014), 3–14; Sb. Math., 205:3 (2014), 307–318
Linking options:
https://www.mathnet.ru/eng/sm8178https://doi.org/10.1070/SM2014v205n03ABEH004377 https://www.mathnet.ru/eng/sm/v205/i3/p3
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Abstract page: | 1131 | Russian version PDF: | 301 | English version PDF: | 24 | References: | 104 | First page: | 106 |
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