Higher regularity of solutions of singular parabolic equations with variable nonlinearity

Higher regularity of solutions of singular parabolic equations with variable nonlinearity Научная публикация

Журнал

Applicable Analysis
ISSN: 0003-6811

Вых. Данные

Год: 2019, Том: 98, Номер: 1-2, Страницы: 310-331 Страниц : 22 DOI: 10.1080/00036811.2017.1382690

Ключевые слова

Nonlinear parabolic equations; regularity of solutions; singular equations; variable nonlinearity

Авторы

Antontsev S. ^1,2 , Shmarev S. ³

Организации

1	CMAF-CIO, University of Lisbon
2	Lavrentyev Institute of Hydrodynamics SB RAS
3	Department of Mathematics, University of Oviedo

We study the global regularity of solutions of the homogeneous Dirichlet problem for the parabolic equation with variable nonlinearity (Formula presented.) where p(x, t), (Formula presented.) are given functions of their arguments, (Formula presented.) and (Formula presented.). Conditions on the data are found that guarantee the existence of a unique strong solution such that (Formula presented.) and (Formula presented.). It is shown that if (Formula presented.) with (Formula presented.), p and (Formula presented.) are Hölder-continuous in (Formula presented.), (Formula presented.) and (Formula presented.), then for every strong solution (Formula presented.) with any (Formula presented.).

Antontsev S. , Shmarev S.
Higher regularity of solutions of singular parabolic equations with variable nonlinearity
Applicable Analysis. 2019. V.98. N1-2. P.310-331. DOI: 10.1080/00036811.2017.1382690 WOS Scopus РИНЦ OpenAlex

≡ Web of science:	WOS:000458651400015
≡ Scopus:	2-s2.0-85030560989
≡ РИНЦ:	41773145
≡ OpenAlex:	W2760819725