Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term

Doan Thi Nhu Quynh; Nguyen Huu Nhan; Le Thi Phuong Ngoc; Nguyen Thanh Long

Applications of Mathematics (2023)

  • Volume: 68, Issue: 2, page 209-254
  • ISSN: 0862-7940

Abstract

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We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable conditions to obtain the global solution, we prove the general decay property with positive initial energy for this global solution.

How to cite

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Quynh, Doan Thi Nhu, et al. "Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term." Applications of Mathematics 68.2 (2023): 209-254. <http://eudml.org/doc/299539>.

@article{Quynh2023,
abstract = {We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable conditions to obtain the global solution, we prove the general decay property with positive initial energy for this global solution.},
author = {Quynh, Doan Thi Nhu, Nhan, Nguyen Huu, Ngoc, Le Thi Phuong, Long, Nguyen Thanh},
journal = {Applications of Mathematics},
keywords = {viscoelastic equations; strong damping; nonlinear memory; general decay},
language = {eng},
number = {2},
pages = {209-254},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term},
url = {http://eudml.org/doc/299539},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Quynh, Doan Thi Nhu
AU - Nhan, Nguyen Huu
AU - Ngoc, Le Thi Phuong
AU - Long, Nguyen Thanh
TI - Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 2
SP - 209
EP - 254
AB - We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable conditions to obtain the global solution, we prove the general decay property with positive initial energy for this global solution.
LA - eng
KW - viscoelastic equations; strong damping; nonlinear memory; general decay
UR - http://eudml.org/doc/299539
ER -

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