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: St. Petersburg Mathematical Journal, Vol. 31, No. 2, 2020, p. 273-296.

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

BibTeX

@article{e89511d35f4a4d1eba00b096bcd0d3f3,

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{"} when crossing this curve. The two-phase conditions are given on this curve and the Cauchy-Dirichlet 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 = "Global solvability, Parabolic systems, Sstrong nonlinearity",

author = "Arkhipova, {A. A.}",

year = "2020",

doi = "10.1090/spmj/1596",

language = "English",

volume = "31",

pages = "273--296",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

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.

PY - 2020

Y1 - 2020

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" when crossing this curve. The two-phase conditions are given on this curve and the Cauchy-Dirichlet 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" when crossing this curve. The two-phase conditions are given on this curve and the Cauchy-Dirichlet 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 - Global solvability

KW - Parabolic systems

KW - Sstrong nonlinearity

UR - http://www.scopus.com/inward/record.url?scp=85090378659&partnerID=8YFLogxK

U2 - 10.1090/spmj/1596

DO - 10.1090/spmj/1596

M3 - Article

AN - SCOPUS:85090378659

VL - 31

SP - 273

EP - 296

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 78033062