Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term

Mama Abdelli; Abderrahmane Beniani; Nadia Mezouar; Ahmed Chahtou

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 1, page 11-34
  • ISSN: 0862-7959

Abstract

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We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as t → ∞ by applying the Lyapunov method.

How to cite

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Abdelli, Mama, et al. "Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term." Mathematica Bohemica 148.1 (2023): 11-34. <http://eudml.org/doc/299556>.

@article{Abdelli2023,
abstract = {We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as $t\rightarrow \infty $ by applying the Lyapunov method.},
author = {Abdelli, Mama, Beniani, Abderrahmane, Mezouar, Nadia, Chahtou, Ahmed},
journal = {Mathematica Bohemica},
keywords = {nonlinear higher-order hyperbolic equation; nonlinear source term; global existence},
language = {eng},
number = {1},
pages = {11-34},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term},
url = {http://eudml.org/doc/299556},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Abdelli, Mama
AU - Beniani, Abderrahmane
AU - Mezouar, Nadia
AU - Chahtou, Ahmed
TI - Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 1
SP - 11
EP - 34
AB - We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as $t\rightarrow \infty $ by applying the Lyapunov method.
LA - eng
KW - nonlinear higher-order hyperbolic equation; nonlinear source term; global existence
UR - http://eudml.org/doc/299556
ER -

References

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