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

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

Journal

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

Output data

Year: 2018, Volume: 466, Number: 1, Pages: 238-263 Pages count : 26 DOI: 10.1016/j.jmaa.2018.05.075

Tags

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

Authors

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

Affiliations

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
Elibrary:	35761485
OpenAlex:	W2806719249

DB	Citing
Scopus	20
OpenAlex	20
Elibrary	22
Web of science	19