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Global higher regularity of solutions to singular p(x,t)-parabolic equations. / Antontsev, Stanislav; Kuznetsov, Ivan; Shmarev, Sergey.

In: Journal of Mathematical Analysis and Applications, Vol. 466, No. 1, 01.10.2018, p. 238-263.

Research output: Contribution to journal › Article › peer-review

Harvard

Antontsev, S, Kuznetsov, I & Shmarev, S 2018, 'Global higher regularity of solutions to singular p(x,t)-parabolic equations', Journal of Mathematical Analysis and Applications, vol. 466, no. 1, pp. 238-263. https://doi.org/10.1016/j.jmaa.2018.05.075

APA

Antontsev, S., Kuznetsov, I., & Shmarev, S. (2018). Global higher regularity of solutions to singular p(x,t)-parabolic equations. Journal of Mathematical Analysis and Applications, 466(1), 238-263. https://doi.org/10.1016/j.jmaa.2018.05.075

Vancouver

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 Oct 1;466(1):238-263. doi: 10.1016/j.jmaa.2018.05.075

Author

Antontsev, Stanislav ; Kuznetsov, Ivan ; Shmarev, Sergey. / Global higher regularity of solutions to singular p(x,t)-parabolic equations. In: Journal of Mathematical Analysis and Applications. 2018 ; Vol. 466, No. 1. pp. 238-263.

BibTeX

@article{d744615fdfca4d89846a76b3652f4491,
title = "Global higher regularity of solutions to singular p(x,t)-parabolic equations",
abstract = "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).",
keywords = "Higher regularity, Singular parabolic equation, Strong solutions, Variable nonlinearity, P-LAPLACIAN, CONTINUITY, PARABOLIC EQUATIONS",
author = "Stanislav Antontsev and Ivan Kuznetsov and Sergey Shmarev",
note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",
year = "2018",
month = oct,
day = "1",
doi = "10.1016/j.jmaa.2018.05.075",
language = "English",
volume = "466",
pages = "238--263",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - Global higher regularity of solutions to singular p(x,t)-parabolic equations

AU - Antontsev, Stanislav

AU - Kuznetsov, Ivan

AU - Shmarev, Sergey

N1 - Publisher Copyright: © 2018 Elsevier Inc.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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).

AB - 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).

KW - Higher regularity

KW - Singular parabolic equation

KW - Strong solutions

KW - Variable nonlinearity

KW - P-LAPLACIAN

KW - CONTINUITY

KW - PARABOLIC EQUATIONS

UR - http://www.scopus.com/inward/record.url?scp=85048151186&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2018.05.075

DO - 10.1016/j.jmaa.2018.05.075

M3 - Article

AN - SCOPUS:85048151186

VL - 466

SP - 238

EP - 263

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -

ID: 13794311