On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms

Bui Duc Nam; Nguyen Huu Nhan; Le Thi Phuong Ngoc; Nguyen Thanh Long

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 2, page 237-270
  • ISSN: 0862-7959

Abstract

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We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.

How to cite

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Nam, Bui Duc, et al. "On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms." Mathematica Bohemica 147.2 (2022): 237-270. <http://eudml.org/doc/298034>.

@article{Nam2022,
abstract = {We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.},
author = {Nam, Bui Duc, Nhan, Nguyen Huu, Ngoc, Le Thi Phuong, Long, Nguyen Thanh},
journal = {Mathematica Bohemica},
keywords = {system of nonlinear wave equations of Kirchhoff-Carrier type; Balakrishnan-Taylor term; Faedo-Galerkin method; local existence; exponential decay},
language = {eng},
number = {2},
pages = {237-270},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms},
url = {http://eudml.org/doc/298034},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Nam, Bui Duc
AU - Nhan, Nguyen Huu
AU - Ngoc, Le Thi Phuong
AU - Long, Nguyen Thanh
TI - On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 2
SP - 237
EP - 270
AB - We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.
LA - eng
KW - system of nonlinear wave equations of Kirchhoff-Carrier type; Balakrishnan-Taylor term; Faedo-Galerkin method; local existence; exponential decay
UR - http://eudml.org/doc/298034
ER -

References

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