Abstract:
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)×Ω(0,T)×Ω, where ΩΩ is a bounded domain. The parabolic
term in the equation has the form (β(x,u))t(β(x,u))t and is determined by the function
β(x,r)∈L1(Ω)β(x,r)∈L1(Ω), where r∈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.
Keywords:
anisotropic parabolic equation, renormalized solution, variable nonlinearity exponents,
existence of a solution.
Citation:
F. Kh. Mukminov, “Existence of a renormalized solution to an anisotropic parabolic problem with
variable nonlinearity exponents”, Sb. Math., 209:5 (2018), 714–738
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\by F.~Kh.~Mukminov
\paper Existence of a~renormalized solution to an anisotropic parabolic problem with
variable nonlinearity exponents
\jour Sb. Math.
\yr 2018
\vol 209
\issue 5
\pages 714--738
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Linking options:
https://www.mathnet.ru/eng/sm8921
https://doi.org/10.1070/SM8921
https://www.mathnet.ru/eng/sm/v209/i5/p120
This publication is cited in the following 9 articles:
Z. Chen, B. Shen, “The existence of entropy solutions for a class of parabolic equations”, Mathematics, 11:17 (2023), 3753
Rakesh Arora, Sergey Shmarev, “Existence and global second-order regularity for anisotropic parabolic equations with variable growth”, Journal of Differential Equations, 349 (2023), 83
Chrif M., Manouni S.E., Hjiaj H., “On the Study of Strongly Parabolic Problems Involving Anisotropic Operators in l-1”, Mon.heft. Math., 195:4 (2021), 611–647
Kozhevnikova L.M., “On Solutions of Anisotropic Elliptic Equations With Variable Exponent and Measure Data”, Complex Var. Elliptic Equ., 65:3 (2020), 333–367
V. F. Vil'danova, “Existence and uniqueness of a weak solution of an integro-differential aggregation equation on a Riemannian manifold”, Sb. Math., 211:2 (2020), 226–257
A. K. Gushchin, “Extensions of the space of continuous functions and embedding theorems”, Sb. Math., 211:11 (2020), 1551–1567
F. Kh. Mukminov, “Existence and Uniqueness of Renormalized Solutions to Parabolic Problems for Equations with Diffuse Measure”, J Math Sci, 247:6 (2020), 900
A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752
F. Kh. Mukminov, “Existence of a Renormalized Solution to an Anisotropic Parabolic Problem for an Equation with Diffuse Measure”, Proc. Steklov Inst. Math., 306 (2019), 178–195
Citation in format AMSBIB
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