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Blow-up for a pseudo-parabolic equation with variable nonlinearity depending on (x,t) and negative initial energy. / Antontsev, Stanislav; Kuznetsov, Ivan; Shmarev, Sergey.

в: Nonlinear Analysis: Real World Applications, Том 71, 103837, 06.2023.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Antontsev, S, Kuznetsov, I & Shmarev, S 2023, 'Blow-up for a pseudo-parabolic equation with variable nonlinearity depending on (x,t) and negative initial energy', Nonlinear Analysis: Real World Applications, Том. 71, 103837. https://doi.org/10.1016/j.nonrwa.2023.103837

APA

Antontsev, S., Kuznetsov, I., & Shmarev, S. (2023). Blow-up for a pseudo-parabolic equation with variable nonlinearity depending on (x,t) and negative initial energy. Nonlinear Analysis: Real World Applications, 71, [103837]. https://doi.org/10.1016/j.nonrwa.2023.103837

Vancouver

Antontsev S, Kuznetsov I, Shmarev S. Blow-up for a pseudo-parabolic equation with variable nonlinearity depending on (x,t) and negative initial energy. Nonlinear Analysis: Real World Applications. 2023 июнь;71:103837. doi: 10.1016/j.nonrwa.2023.103837

Author

Antontsev, Stanislav ; Kuznetsov, Ivan ; Shmarev, Sergey. / Blow-up for a pseudo-parabolic equation with variable nonlinearity depending on (x,t) and negative initial energy. в: Nonlinear Analysis: Real World Applications. 2023 ; Том 71.

BibTeX

@article{e9372f8bafe64be194e5123d05347075,
title = "Blow-up for a pseudo-parabolic equation with variable nonlinearity depending on (x,t) and negative initial energy",
abstract = "We study the Dirichlet problem for the pseudo-parabolic equation ut−diva(x,t)|∇u|p(x,t)−2∇u−Δut=b(x,t)|u|q(x,t)−2uin the cylinder QT=Ω×(0,T), where Ω⊂Rd is a sufficiently smooth domain. The positive coefficients a, b and the exponents p≥2, q>2 are given Lipschitz-continuous functions. The functions a, p are monotone decreasing, and b, q are monotone increasing in t. It is shown that there exists a positive constant M=M(|Ω|,sup(x,t)∈QTp(x,t),sup(x,t)∈QTq(x,t)), such if the initial energy is negative, E(0)=∫Ω[Formula presented]|∇u0(x)|p(x,0)−[Formula presented]|u0(x)|q(x,0)dx",
keywords = "Blow-up, Local solution, Pseudo-parabolic equation, Variable nonlinearity",
author = "Stanislav Antontsev and Ivan Kuznetsov and Sergey Shmarev",
note = "The authors would like to thank the anonymous referees for their valuable remarks and recommendations that helped improve the earlier version of the paper. The first and second authors are supported by the State Assignment of the Russian Ministry of Science and Higher Education under project no. FWGG-2021-0010 , Russian Federation. The third author acknowledges the support of the Research Grant MCI-21-PID2020-116287GB-I00, Spain.",
year = "2023",
month = jun,
doi = "10.1016/j.nonrwa.2023.103837",
language = "English",
volume = "71",
journal = "Nonlinear Analysis: Real World Applications",
issn = "1468-1218",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Blow-up for a pseudo-parabolic equation with variable nonlinearity depending on (x,t) and negative initial energy

AU - Antontsev, Stanislav

AU - Kuznetsov, Ivan

AU - Shmarev, Sergey

N1 - The authors would like to thank the anonymous referees for their valuable remarks and recommendations that helped improve the earlier version of the paper. The first and second authors are supported by the State Assignment of the Russian Ministry of Science and Higher Education under project no. FWGG-2021-0010 , Russian Federation. The third author acknowledges the support of the Research Grant MCI-21-PID2020-116287GB-I00, Spain.

PY - 2023/6

Y1 - 2023/6

N2 - We study the Dirichlet problem for the pseudo-parabolic equation ut−diva(x,t)|∇u|p(x,t)−2∇u−Δut=b(x,t)|u|q(x,t)−2uin the cylinder QT=Ω×(0,T), where Ω⊂Rd is a sufficiently smooth domain. The positive coefficients a, b and the exponents p≥2, q>2 are given Lipschitz-continuous functions. The functions a, p are monotone decreasing, and b, q are monotone increasing in t. It is shown that there exists a positive constant M=M(|Ω|,sup(x,t)∈QTp(x,t),sup(x,t)∈QTq(x,t)), such if the initial energy is negative, E(0)=∫Ω[Formula presented]|∇u0(x)|p(x,0)−[Formula presented]|u0(x)|q(x,0)dx

AB - We study the Dirichlet problem for the pseudo-parabolic equation ut−diva(x,t)|∇u|p(x,t)−2∇u−Δut=b(x,t)|u|q(x,t)−2uin the cylinder QT=Ω×(0,T), where Ω⊂Rd is a sufficiently smooth domain. The positive coefficients a, b and the exponents p≥2, q>2 are given Lipschitz-continuous functions. The functions a, p are monotone decreasing, and b, q are monotone increasing in t. It is shown that there exists a positive constant M=M(|Ω|,sup(x,t)∈QTp(x,t),sup(x,t)∈QTq(x,t)), such if the initial energy is negative, E(0)=∫Ω[Formula presented]|∇u0(x)|p(x,0)−[Formula presented]|u0(x)|q(x,0)dx

KW - Blow-up

KW - Local solution

KW - Pseudo-parabolic equation

KW - Variable nonlinearity

UR - https://www.scopus.com/inward/record.url?eid=2-s2.0-85146643740&partnerID=40&md5=86bb2dcb0021f460ba7cc1c473a80ecd

UR - https://www.mendeley.com/catalogue/f6207bde-0f3b-3678-9085-b639edc5175a/

U2 - 10.1016/j.nonrwa.2023.103837

DO - 10.1016/j.nonrwa.2023.103837

M3 - Article

VL - 71

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

M1 - 103837

ER -

ID: 49082245