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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 236–248 (Mi semr1056)  

Differentical equations, dynamical systems and optimal control

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

T. V. Sazhenkovaa, S. A. Sazhenkovbc

a Department of Mathematics & Information Technologies, Altai State University, 61, Lenina ave., Barnaul, 656049, Russia
b Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, 15, Acad. Lavrentyeva ave., Novosibirsk, 630090, Russia
c Mechanical & Mathematical Department, Novosibirsk National Research State University, 2, Pirogova str., Novosibirsk, 630090, Russia

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 Hölder's spaces via systematic study of structure of the penalty operator.

Keywords: penalty method, p-Laplace operator, diffusion-absorption equation, one-sided constraint.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00649_a
Ministry of Education and Science of the Russian Federation III.22.4.2
The work was supported by the Ministry of Higher Education and Science of the Russian Federation (project no. III.22.4.2) and by the Russian Foundation for Basic Research (grant no. 18-01-00649).


DOI: https://doi.org/10.33048/semi.2019.16.015

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Document Type: Article
UDC: 517.972.5 + 51-72
MSC: 35J92
Received January 17, 2019, published February 21, 2019
Language: English

Citation: T. V. Sazhenkova, S. A. Sazhenkov, “Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint”, Sib. Èlektron. Mat. Izv., 16 (2019), 236–248

Citation in format AMSBIB
\Bibitem{SazSaz19}
\by T.~V.~Sazhenkova, S.~A.~Sazhenkov
\paper Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 236--248
\mathnet{http://mi.mathnet.ru/semr1056}
\crossref{https://doi.org/10.33048/semi.2019.16.015}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000462268100015}


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