Geodesic
Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term
Applications of Mathematics, Tome 68 (2023) no. 2, pp. 209-254.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.\looseness -1
DOI : 10.21136/AM.2022.0200-21
Classification : 35L20, 35L70
Keywords: viscoelastic equations; strong damping; nonlinear memory; general decay 
@article{10_21136_AM_2022_0200_21,
     author = {Quynh, Doan Thi Nhu and Nhan, Nguyen Huu and Ngoc, Le Thi Phuong and Long, Nguyen Thanh},
     title = {Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term},
     journal = {Applications of Mathematics},
     pages = {209--254},
     publisher = {mathdoc},
     volume = {68},
     number = {2},
     year = {2023},
     doi = {10.21136/AM.2022.0200-21},
     mrnumber = {4574654},
     zbl = {07675567},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0200-21/}
}
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
SP  - 209
EP  - 254
VL  - 68
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0200-21/
DO  - 10.21136/AM.2022.0200-21
LA  - en
ID  - 10_21136_AM_2022_0200_21
ER  - 
%0 Journal Article
%A Quynh, Doan Thi Nhu
%A Nhan, Nguyen Huu
%A Ngoc, Le Thi Phuong
%A Long, Nguyen Thanh
%T Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term
%J Applications of Mathematics
%D 2023
%P 209-254
%V 68
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0200-21/
%R 10.21136/AM.2022.0200-21
%G en
%F 10_21136_AM_2022_0200_21
Quynh, Doan Thi Nhu; Nhan, Nguyen Huu; Ngoc, Le Thi Phuong; Long, Nguyen Thanh. Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term. Applications of Mathematics, Tome 68 (2023) no. 2, pp. 209-254. doi : 10.21136/AM.2022.0200-21. http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0200-21/

Cité par Sources :