Standard

Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint. / Sazhenkova, Tatiana V.; Sazhenkov, Sergey A.

In: Сибирские электронные математические известия, Vol. 16, 01.01.2019, p. 236-248.

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

Harvard

Sazhenkova, TV & Sazhenkov, SA 2019, 'Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint', Сибирские электронные математические известия, vol. 16, pp. 236-248. https://doi.org/10.33048/semi.2019.16.015

APA

Sazhenkova, T. V., & Sazhenkov, S. A. (2019). Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint. Сибирские электронные математические известия, 16, 236-248. https://doi.org/10.33048/semi.2019.16.015

Vancouver

Sazhenkova TV, Sazhenkov SA. Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint. Сибирские электронные математические известия. 2019 Jan 1;16:236-248. doi: 10.33048/semi.2019.16.015

Author

Sazhenkova, Tatiana V. ; Sazhenkov, Sergey A. / Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint. In: Сибирские электронные математические известия. 2019 ; Vol. 16. pp. 236-248.

BibTeX

@article{06d7c15ed78b4a95bc1c608f8b434f1b,
title = "Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint",
abstract = "We consider the homogeneous Dirichlet problem for the nonlinear diffusion-absorption equation with a one-sided constraint imposed on diffusion flux values. The family of approximate solutions constructed by means of Alexander Kaplan's integral penalty operator is studied. It is shown that this family converges weakly in the first-order Sobolev space to the solution of the original problem, as the small regularization parameter tends to zero. Thereafter, a property of uniform approximation of solutions is established in H{\"o}lder's spaces via systematic study of structure of the penalty operator.",
keywords = "Diffusion-absorption equation, One-sided constraint, P-Laplace operator, Penalty method, one-sided constraint, OF-WAR GAMES, penalty method, p-Laplace operator, diffusion-absorption equation",
author = "Sazhenkova, {Tatiana V.} and Sazhenkov, {Sergey A.}",
year = "2019",
month = jan,
day = "1",
doi = "10.33048/semi.2019.16.015",
language = "English",
volume = "16",
pages = "236--248",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint

AU - Sazhenkova, Tatiana V.

AU - Sazhenkov, Sergey A.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider the homogeneous Dirichlet problem for the nonlinear diffusion-absorption equation with a one-sided constraint imposed on diffusion flux values. The family of approximate solutions constructed by means of Alexander Kaplan's integral penalty operator is studied. It is shown that this family converges weakly in the first-order Sobolev space to the solution of the original problem, as the small regularization parameter tends to zero. Thereafter, a property of uniform approximation of solutions is established in Hölder's spaces via systematic study of structure of the penalty operator.

AB - We consider the homogeneous Dirichlet problem for the nonlinear diffusion-absorption equation with a one-sided constraint imposed on diffusion flux values. The family of approximate solutions constructed by means of Alexander Kaplan's integral penalty operator is studied. It is shown that this family converges weakly in the first-order Sobolev space to the solution of the original problem, as the small regularization parameter tends to zero. Thereafter, a property of uniform approximation of solutions is established in Hölder's spaces via systematic study of structure of the penalty operator.

KW - Diffusion-absorption equation

KW - One-sided constraint

KW - P-Laplace operator

KW - Penalty method

KW - one-sided constraint

KW - OF-WAR GAMES

KW - penalty method

KW - p-Laplace operator

KW - diffusion-absorption equation

UR - http://www.scopus.com/inward/record.url?scp=85071177147&partnerID=8YFLogxK

U2 - 10.33048/semi.2019.16.015

DO - 10.33048/semi.2019.16.015

M3 - Article

AN - SCOPUS:85071177147

VL - 16

SP - 236

EP - 248

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 21346534