This article is cited in 3 scientific papers (total in 3 papers)
Research Papers
Weak global solvability of the two-phase problem for a class of parabolic systems with strong nonlinearity in the gradient. The case of two spatial variables
Abstract:
A class of quasilinear parabolic systems with nondiagonal principal matrix and strongly nonlinear additional terms is considered. The elliptic operator of the system has a variational structure and is generated by a quadratic functional with a nondiagonal matrix. A plane domain of the spatial variables is divided by a smooth curve in two subdomains and the principal matrix of the system has a “jump” when crossing this curve. The two-phase conditions are given on this curve and the Cauchy-Dirichlet conditions hold at the parabolic boundary of the main parabolic cylinder. The existence of a weak Hölder continuous global solution of the two-phase problem is proved. The problem can be regarded as a construction of the heat flow from a given vector-function to an extremal of the functional.
Keywords:
parabolic systems, strong nonlinearity, global solvability.
Citation:
A. A. Arkhipova, “Weak global solvability of the two-phase problem for a class of parabolic systems with strong nonlinearity in the gradient. The case of two spatial variables”, Algebra i Analiz, 31:2 (2019), 118–151; St. Petersburg Math. J., 31:2 (2019), 273–296
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\pages 118--151
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Linking options:
https://www.mathnet.ru/eng/aa1640
https://www.mathnet.ru/eng/aa/v31/i2/p118
This publication is cited in the following 3 articles:
A. A. Arkhipova, “Quasilinear Elliptic and Parabolic Systems with Nondiagonal Principal Matrices and Strong Nonlinearities in the Gradient. Solvability and Regularity Problems”, J Math Sci, 2024
A. A. Arkhipova, “Kvazilineinye ellipticheskie i parabolicheskie sistemy s nediagonalnymi glavnymi matritsami i silnymi nelineinostyami po gradientu. Problemy razreshimosti i regulyarnosti”, SMFN, 69, no. 1, Rossiiskii universitet druzhby narodov, M., 2023, 18–31
A. A. Arkhipova, “Global Solvability of the Cauchy-Dirichlet Problem for a Class of Strongly Nonlinear Parabolic Systems”, J Math Sci, 250:2 (2020), 201
Citation in format AMSBIB
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