Global higher regularity of solutions to singular p(x,t)-parabolic equations | Sciact

Global higher regularity of solutions to singular p(x,t)-parabolic equations Научная публикация

Журнал

Journal of Mathematical Analysis and Applications
ISSN: 0022-247X

Вых. Данные

Год: 2018, Том: 466, Номер: 1, Страницы: 238-263 Страниц : 26 DOI: 10.1016/j.jmaa.2018.05.075

Ключевые слова

Higher regularity; Singular parabolic equation; Strong solutions; Variable nonlinearity

Авторы

Antontsev Stanislav ^1,2,3 , Kuznetsov Ivan ^2,3 , Shmarev Sergey ⁴

Организации

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

We study the homogeneous Dirichlet problem for the equation ut=div(|∇u|p(x,t)−2∇u)+f(x,t,u) in the cylinder QT=Ω×(0,T), Ω⊂Rd, d≥2. It is assumed that p(x,t)∈([Formula presented],2) and |∇p|, |pt| are bounded a.e. in QT. We find conditions on p(x,t), f(x,t,u) and u(x,0) sufficient for the existence of strong solutions, local or global in time. It is proven that the strong solutions possess the property of global higher regularity: ut∈L2(QT), |∇u|∈L∞(0,T;L2(Ω)), |Dij 2u|p(x,t)∈L1(QT).

Antontsev S. , Kuznetsov I. , Shmarev S.
Global higher regularity of solutions to singular p(x,t)-parabolic equations
Journal of Mathematical Analysis and Applications. 2018. V.466. N1. P.238-263. DOI: 10.1016/j.jmaa.2018.05.075 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000438327400013
Scopus:	2-s2.0-85048151186
РИНЦ:	35761485
OpenAlex:	W2806719249

БД	Цитирований
Scopus	17
OpenAlex	19
РИНЦ	19
Web of science	18