Regularity of solutions to a model oblique derivative problem for quasilinear parabolic systems with nondiagonal principal matrices

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Regularity of solutions to a model oblique derivative problem for quasilinear parabolic systems with nondiagonal principal matrices. / Arkhipova, A. A. ; Grishina, G. V. .

In: Vestnik St.Petersburg University, Vol. 52, No. 1, 2019, p. 1-18.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{66a37610bdbf4884bca1f21d682afd92,

title = "Regularity of solutions to a model oblique derivative problem for quasilinear parabolic systems with nondiagonal principal matrices",

abstract = "We consider quasilinear parabolic systems of equations with nondiagonal principal matrices. The oblique derivative of a solution is defined on the plane part of the lateral surface of a parabolic cylinder. We do not assume smoothness of the principal matrix and the boundary functions in the time variable and prove partial H{\"o}lder continuity of a weak solution near the plane part of the lateral surface of the cylinder. H{\"o}lder continuity of weak solutions to the correspondent linear problem is stated. A modification of the A(t)-caloric approximation method is applied to study the regularity of weak solutions.",

keywords = "nonlinearity, oblique derivative, parabolic systems, regularity",

author = "Arkhipova, {A. A.} and Grishina, {G. V.}",

note = "Arkhipova, A.A. & Grishina, G.V. Vestnik St.Petersb. Univ.Math. (2019) 52: 1. https://proxy.library.spbu.ru:2060/10.3103/S1063454119010023",

year = "2019",

doi = "10.3103/s1063454119010023",

language = "English",

volume = "52",

pages = "1--18",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Regularity of solutions to a model oblique derivative problem for quasilinear parabolic systems with nondiagonal principal matrices

AU - Arkhipova, A. A.

AU - Grishina, G. V.

N1 - Arkhipova, A.A. & Grishina, G.V. Vestnik St.Petersb. Univ.Math. (2019) 52: 1. https://proxy.library.spbu.ru:2060/10.3103/S1063454119010023

PY - 2019

Y1 - 2019

N2 - We consider quasilinear parabolic systems of equations with nondiagonal principal matrices. The oblique derivative of a solution is defined on the plane part of the lateral surface of a parabolic cylinder. We do not assume smoothness of the principal matrix and the boundary functions in the time variable and prove partial Hölder continuity of a weak solution near the plane part of the lateral surface of the cylinder. Hölder continuity of weak solutions to the correspondent linear problem is stated. A modification of the A(t)-caloric approximation method is applied to study the regularity of weak solutions.

AB - We consider quasilinear parabolic systems of equations with nondiagonal principal matrices. The oblique derivative of a solution is defined on the plane part of the lateral surface of a parabolic cylinder. We do not assume smoothness of the principal matrix and the boundary functions in the time variable and prove partial Hölder continuity of a weak solution near the plane part of the lateral surface of the cylinder. Hölder continuity of weak solutions to the correspondent linear problem is stated. A modification of the A(t)-caloric approximation method is applied to study the regularity of weak solutions.

KW - nonlinearity

KW - oblique derivative

KW - parabolic systems

KW - regularity

UR - http://www.scopus.com/inward/record.url?scp=85064894127&partnerID=8YFLogxK

U2 - 10.3103/s1063454119010023

DO - 10.3103/s1063454119010023

M3 - Article

VL - 52

SP - 1

EP - 18

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 38494738