Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition

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Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition. / Arkhipova, A. A. ; Grishina, G. V. .

In: Journal of Mathematical Sciences (United States), Vol. 232, No. 3, 07.2018, p. 232-253.

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

BibTeX

@article{09315ef265af4c71b93a9969eaae8386,

title = "Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition",

abstract = "We consider a quasilinear parabolic system of equations with nondiagonal principal matrix in a model parabolic cylinder with the Neumann condition on the plane part Γ of the lateral surface of the cylinder. We prove the partial regularity (the H{\"o}lder continuity) of the weak solution in a neighborhood of Γ by the method of A(t)-caloric approximations adapted to the problem with the Neumann boundary condition.",

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

note = "Arkhipova, A.A., Grishina, G.V. Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition. J Math Sci 232, 232–253 (2018). https://doi.org/10.1007/s10958-018-3871-4",

year = "2018",

month = jul,

doi = "10.1007/s10958-018-3871-4",

language = "English",

volume = "232",

pages = "232--253",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition

AU - Arkhipova, A. A.

AU - Grishina, G. V.

N1 - Arkhipova, A.A., Grishina, G.V. Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition. J Math Sci 232, 232–253 (2018). https://doi.org/10.1007/s10958-018-3871-4

PY - 2018/7

Y1 - 2018/7

N2 - We consider a quasilinear parabolic system of equations with nondiagonal principal matrix in a model parabolic cylinder with the Neumann condition on the plane part Γ of the lateral surface of the cylinder. We prove the partial regularity (the Hölder continuity) of the weak solution in a neighborhood of Γ by the method of A(t)-caloric approximations adapted to the problem with the Neumann boundary condition.

AB - We consider a quasilinear parabolic system of equations with nondiagonal principal matrix in a model parabolic cylinder with the Neumann condition on the plane part Γ of the lateral surface of the cylinder. We prove the partial regularity (the Hölder continuity) of the weak solution in a neighborhood of Γ by the method of A(t)-caloric approximations adapted to the problem with the Neumann boundary condition.

UR - http://www.scopus.com/inward/record.url?scp=85047901486&partnerID=8YFLogxK

U2 - 10.1007/s10958-018-3871-4

DO - 10.1007/s10958-018-3871-4

M3 - Article

VL - 232

SP - 232

EP - 253

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -

ID: 28233353