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On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator. / Antontsev, Stanislav; Shmarev, Sergey.

In: Nonlinear Analysis: Real World Applications, Vol. 56, 103165, 01.12.2020.

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

Harvard

Antontsev, S & Shmarev, S 2020, 'On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator', Nonlinear Analysis: Real World Applications, vol. 56, 103165. https://doi.org/10.1016/j.nonrwa.2020.103165

APA

Antontsev, S., & Shmarev, S. (2020). On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator. Nonlinear Analysis: Real World Applications, 56, [103165]. https://doi.org/10.1016/j.nonrwa.2020.103165

Vancouver

Antontsev S, Shmarev S. On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator. Nonlinear Analysis: Real World Applications. 2020 Dec 1;56:103165. doi: 10.1016/j.nonrwa.2020.103165

Author

Antontsev, Stanislav ; Shmarev, Sergey. / On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator. In: Nonlinear Analysis: Real World Applications. 2020 ; Vol. 56.

BibTeX

@article{4223e8a15ba24aca8d1ee1321622147e,
title = "On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator",
abstract = "We study the homogeneous Dirichlet problem for a class of nonlocal singular parabolic equations ut−div|∇u|p[u]−2∇u=fin Ω×(0,T),where Ω⊂Rd, d≥2, is a smooth bounded domain, p[u]=p(l(u)) is a given function with values in the interval [p−,p+]⊂(1,2), and l(u)=∫Ω|u(x,t)|αdx, α∈[1,2], is a functional of the unknown solution. We find sufficient conditions for global or local in time solvability of the problem, prove the uniqueness, and show that every solution gets extinct in a finite time.",
keywords = "Nonlocal equation, Singular parabolic equation, Strong solutions, Variable nonlinearity, P(U)-LAPLACIAN, VARIABLE EXPONENT, UNIQUENESS",
author = "Stanislav Antontsev and Sergey Shmarev",
year = "2020",
month = dec,
day = "1",
doi = "10.1016/j.nonrwa.2020.103165",
language = "English",
volume = "56",
journal = "Nonlinear Analysis: Real World Applications",
issn = "1468-1218",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator

AU - Antontsev, Stanislav

AU - Shmarev, Sergey

PY - 2020/12/1

Y1 - 2020/12/1

N2 - We study the homogeneous Dirichlet problem for a class of nonlocal singular parabolic equations ut−div|∇u|p[u]−2∇u=fin Ω×(0,T),where Ω⊂Rd, d≥2, is a smooth bounded domain, p[u]=p(l(u)) is a given function with values in the interval [p−,p+]⊂(1,2), and l(u)=∫Ω|u(x,t)|αdx, α∈[1,2], is a functional of the unknown solution. We find sufficient conditions for global or local in time solvability of the problem, prove the uniqueness, and show that every solution gets extinct in a finite time.

AB - We study the homogeneous Dirichlet problem for a class of nonlocal singular parabolic equations ut−div|∇u|p[u]−2∇u=fin Ω×(0,T),where Ω⊂Rd, d≥2, is a smooth bounded domain, p[u]=p(l(u)) is a given function with values in the interval [p−,p+]⊂(1,2), and l(u)=∫Ω|u(x,t)|αdx, α∈[1,2], is a functional of the unknown solution. We find sufficient conditions for global or local in time solvability of the problem, prove the uniqueness, and show that every solution gets extinct in a finite time.

KW - Nonlocal equation

KW - Singular parabolic equation

KW - Strong solutions

KW - Variable nonlinearity

KW - P(U)-LAPLACIAN

KW - VARIABLE EXPONENT

KW - UNIQUENESS

UR - http://www.scopus.com/inward/record.url?scp=85085732253&partnerID=8YFLogxK

U2 - 10.1016/j.nonrwa.2020.103165

DO - 10.1016/j.nonrwa.2020.103165

M3 - Article

AN - SCOPUS:85085732253

VL - 56

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

M1 - 103165

ER -

ID: 24411634