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

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

Журнал

Сибирские электронные математические известия / Siberian Electronic Mathematical Reports
ISSN: 1813-3304

Вых. Данные

Год: 2019, Том: 16, Страницы: 236-248 Страниц : 13 DOI: 10.33048/semi.2019.16.015

Ключевые слова

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

Авторы

Sazhenkova T.V. ¹ , Sazhenkov S.A. ^2,3

Организации

1	Altai State University
2	Novosibirsk National Research State University
3	Lavrentyev Institute of Hydrodynamics

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

Sazhenkova T.V. , Sazhenkov S.A.
Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2019. V.16. P.236-248. DOI: 10.33048/semi.2019.16.015 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	17 янв. 2019 г.
Опубликована online:	21 февр. 2019 г.

Web of science:	WOS:000462268100015
Scopus:	2-s2.0-85071177147
РИНЦ:	42735060
OpenAlex:	W3015810356

БД	Цитирований
Scopus	1