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

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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. / Arkhipova, A.A.

In: АЛГЕБРА И АНАЛИЗ, Vol. 31, No. 2, 03.2019, p. 118-151.

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

BibTeX

@article{26b26bba154a4249a3276499fc7faa0b,

title = "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” crossing this curve. The two-phase conditions are given on this curve and the Cauchy–Dirihlet conditions hold at the parabolic boundary of the main parabolic cylinder. The existence of a weak H{\"o}lder 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 = "системы уравнений, параболичность, Parabolic systems, strong nonlinearity, global solvability",

author = "A.A. Arkhipova",

note = "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”, Алгебра и анализ, 31:2 (2019), 118–151",

year = "2019",

month = mar,

language = "English",

volume = "31",

pages = "118--151",

journal = "АЛГЕБРА И АНАЛИЗ",

issn = "0234-0852",

publisher = "Издательство {"}Наука{"}",

number = "2",

}

RIS

TY - JOUR

T1 - 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

AU - Arkhipova, A.A.

N1 - 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”, Алгебра и анализ, 31:2 (2019), 118–151

PY - 2019/3

Y1 - 2019/3

N2 - 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” crossing this curve. The two-phase conditions are given on this curve and the Cauchy–Dirihlet 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.

AB - 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” crossing this curve. The two-phase conditions are given on this curve and the Cauchy–Dirihlet 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.

KW - системы уравнений, параболичность

KW - Parabolic systems

KW - strong nonlinearity

KW - global solvability

UR - http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=aa&paperid=1640&option_lang=rus

UR - https://elibrary.ru/item.asp?id=37078093

M3 - Article

VL - 31

SP - 118

EP - 151

JO - АЛГЕБРА И АНАЛИЗ

JF - АЛГЕБРА И АНАЛИЗ

SN - 0234-0852

IS - 2

ER -

ID: 39997922