Тип публикации: статья из журнала
Год издания: 2024
Аннотация: Let G1,G2 be domains in Rn+1, n≥2, such that G1⊂G2 and the domain G1 have rather regular boundary. We investigate the problem of approximation of solutions to strongly uniformly 2m-parabolic system L in the domain G1 by solutions to the same system in the domain G2. First, we prove that the space SL(G2) of solutions to the system LПоказать полностьюin the domain G2 is dense in the space SL(G1), endowed with the standard Fréchet topology of the uniform convergence on compact subsets in G1, if and only if the complements G2(t)∖G1(t) have no non-empty compact components in G2(t) for each t∈R, where Gj(t)={x∈Rn:(x,t)∈Gj}. Next, under additional assumptions on the regularity of the bounded domains G1 and G1(t), we prove that solutions from the Lebesgue class L2(G1)∩SL(G1) can be approximated by solutions from SL(G2) if and only if the same assumption on the complements G2(t)∖G1(t), t∈R, is fulfilled.
Журнал: Сибирские электронные математические известия
Выпуск журнала: Т. 21, № 1
Номера страниц: 383-404
ISSN журнала: 18133304
Место издания: Новосибирск
Издатель: Институт математики им. С.Л. Соболева СО РАН