Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint Full article
| Journal |
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports
ISSN: 1813-3304 |
||||||
|---|---|---|---|---|---|---|---|
| Output data | Year: 2019, Volume: 16, Pages: 236-248 Pages count : 13 DOI: 10.33048/semi.2019.16.015 | ||||||
| Tags | penalty method, p-Laplace operator, diffusion-absorption equation, one-sided constraint | ||||||
| Authors |
|
||||||
| Affiliations |
|
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 Holder's spaces via systematic study of structure of the penalty operator.
Cite:
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
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
Dates:
| Submitted: | Jan 17, 2019 |
| Published online: | Feb 21, 2019 |
Identifiers:
| Web of science: | WOS:000462268100015 |
| Scopus: | 2-s2.0-85071177147 |
| Elibrary: | 42735060 |
| OpenAlex: | W3015810356 |