Geodesic
Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation
Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 768-786

Voir la notice de l'article provenant de la source Cambridge

DOI

The study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.
DOI : 10.4153/CMB-2018-012-1
Mots-clés : 32H50, 34C28, 37K50, 54H20, 58J45, chaotic vibration, reflection boundary condition, period-doubling bifurcation, method of characteristics 
Li, Liangliang; Tian, Jing; Chen, Goong. Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation. Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 768-786. doi: 10.4153/CMB-2018-012-1
@article{10_4153_CMB_2018_012_1,
     author = {Li, Liangliang and Tian, Jing and Chen, Goong},
     title = {Chaotic {Vibration} of a {Two-dimensional} {Non-strictly} {Hyperbolic} {Equation}},
     journal = {Canadian mathematical bulletin},
     pages = {768--786},
     year = {2018},
     volume = {61},
     number = {4},
     doi = {10.4153/CMB-2018-012-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-012-1/}
}
TY  - JOUR
AU  - Li, Liangliang
AU  - Tian, Jing
AU  - Chen, Goong
TI  - Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation
JO  - Canadian mathematical bulletin
PY  - 2018
SP  - 768
EP  - 786
VL  - 61
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-012-1/
DO  - 10.4153/CMB-2018-012-1
ID  - 10_4153_CMB_2018_012_1
ER  - 
%0 Journal Article
%A Li, Liangliang
%A Tian, Jing
%A Chen, Goong
%T Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation
%J Canadian mathematical bulletin
%D 2018
%P 768-786
%V 61
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-012-1/
%R 10.4153/CMB-2018-012-1
%F 10_4153_CMB_2018_012_1

Cité par Sources :