Regularity of weak solutions to a model problem  with conjugation conditions for quasilinear parabolic systems

A. A.  Arkhipova

Regularity of weak solutions to a model problem with conjugation conditions for quasilinear parabolic systems

A. A. Arkhipova

Кафедра математической физики

Research output

1 Citation (Scopus)

Abstract

We consider a parabolic quasilinear second order system of equations in divergence form in a model parabolic cylinder. We prove the Hölder continuity of a weak solution on a set of full measure in the cylinder. It is shown that the linear system has no singular set. We use a modified method of A-caloric approximation which takes into account the conjugation conditions on the interface between media.

Translated title of the contribution	Регулярность обобщенных решений модельной задачи с условиями сопряжения для квазилинейных параболических систем уравнений
Original language	English
Pages (from-to)	850-873
Number of pages	23
Journal	Journal of Mathematical Sciences
Volume	219
Issue number	6
Early online date	8 Nov 2016
Publication status	Published - 2016

Scopus subject areas

Mathematics(all)

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https://link.springer.com/article/10.1007/s10958-016-3151-0

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title = "Regularity of weak solutions to a model problem with conjugation conditions for quasilinear parabolic systems",

abstract = "We consider a parabolic quasilinear second order system of equations in divergence form in a model parabolic cylinder. We prove the H{\"o}lder continuity of a weak solution on a set of full measure in the cylinder. It is shown that the linear system has no singular set. We use a modified method of A-caloric approximation which takes into account the conjugation conditions on the interface between media.",

keywords = "регулярность решений",

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note = "Arkhipova, A.A. Regularity of Weak Solutions to a Model Problem with Conjugation Conditions for Quasilinear Parabolic Systems of Equations. J Math Sci 219, 850–873 (2016). https://doi.org/10.1007/s10958-016-3151-0",

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Y1 - 2016

N2 - We consider a parabolic quasilinear second order system of equations in divergence form in a model parabolic cylinder. We prove the Hölder continuity of a weak solution on a set of full measure in the cylinder. It is shown that the linear system has no singular set. We use a modified method of A-caloric approximation which takes into account the conjugation conditions on the interface between media.

AB - We consider a parabolic quasilinear second order system of equations in divergence form in a model parabolic cylinder. We prove the Hölder continuity of a weak solution on a set of full measure in the cylinder. It is shown that the linear system has no singular set. We use a modified method of A-caloric approximation which takes into account the conjugation conditions on the interface between media.

KW - регулярность решений

UR - https://link.springer.com/article/10.1007/s10958-016-3151-0

M3 - Article

VL - 219

SP - 850

EP - 873

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -