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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 3, Pages 470–490 (Mi zvmmf10538)  

This article is cited in 2 scientific papers (total in 2 papers)

Regularity of solutions of the model Venttsel' problem for quasilinear parabolic systems with nonsmooth in time principal matrices

A. A. Arkhipova

Saint Petersburg State University

Abstract: The Venttsel' problem in the model statement for quasilinear parabolic systems of equations with nondiagonal principal matrices is considered. It is only assumed that the principal matrices and the boundary condition are bounded with respect to the time variable. The partial smoothness of the weak solutions (Hölder continuity on a set of full measure up to the surface on which the Venttsel' condition is defined) is proved. The proof uses the $A(t)$-caloric approximation method, which was also used in [1] to investigate the regularity of the solution to the corresponding linear problem.

Key words: parabolic system of equations, partial smoothness of weak solutions, $A(t)$-caloric approximation method, Venttsel' problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-07650_а


DOI: https://doi.org/10.7868/S0044466917030036

Full text: PDF file (325 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:3, 476–496

Bibliographic databases:

UDC: 519.63
Received: 26.07.2016

Citation: A. A. Arkhipova, “Regularity of solutions of the model Venttsel' problem for quasilinear parabolic systems with nonsmooth in time principal matrices”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 470–490; Comput. Math. Math. Phys., 57:3 (2017), 476–496

Citation in format AMSBIB
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\pages 470--490
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Arkhipova A.A., Grishina G.V., “Regularity of Solutions to a Model Oblique Derivative Problem For Quasilinear Parabolic Systems With Nondiagonal Principal Matrices”, Vestn. St Petersb. Univ.-Math., 52:1 (2019), 1–18  crossref  mathscinet  isi  scopus
    2. Arkhipova A.A., Stara J., “Regularity Problem For One Class of Nonlinear Parabolic Systems With Non-Smooth in Time Principal Matrices”, Comment. Math. Univ. Carol., 60:2 (2019), 233–269  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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