Geodesic
Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions
Applications of Mathematics, Tome 61 (2016) no. 2, pp. 165-196

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

In this paper we consider a nonlinear Love equation associated with Dirichlet conditions. First, under suitable conditions, the existence of a unique local weak solution is proved. Next, a blow up result for solutions with negative initial energy is also established. Finally, a sufficient condition guaranteeing the global existence and exponential decay of weak solutions is given. The proofs are based on the linearization method, the Galerkin method associated with a priori estimates, weak convergence, compactness techniques and the construction of a suitable Lyapunov functional. To our knowledge, there has been no decay or blow up result for equations of Love waves or Love type waves before.
DOI : 10.1007/s10492-016-0127-9
Classification : 35L20, 35L70, 35Q74, 37B25
Keywords: nonlinear Love equation; Faedo-Galerkin method; local existence; blow up; exponential decay 
@article{10_1007_s10492_016_0127_9,
     author = {Ngoc, Le Thi Phuong and Long, Nguyen Thanh},
     title = {Existence, blow-up and exponential decay for a nonlinear {Love} equation associated with {Dirichlet} conditions},
     journal = {Applications of Mathematics},
     pages = {165--196},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {2016},
     doi = {10.1007/s10492-016-0127-9},
     mrnumber = {3470772},
     zbl = {06562152},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0127-9/}
}
TY  - JOUR
AU  - Ngoc, Le Thi Phuong
AU  - Long, Nguyen Thanh
TI  - Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions
JO  - Applications of Mathematics
PY  - 2016
SP  - 165
EP  - 196
VL  - 61
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0127-9/
DO  - 10.1007/s10492-016-0127-9
LA  - en
ID  - 10_1007_s10492_016_0127_9
ER  - 
%0 Journal Article
%A Ngoc, Le Thi Phuong
%A Long, Nguyen Thanh
%T Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions
%J Applications of Mathematics
%D 2016
%P 165-196
%V 61
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0127-9/
%R 10.1007/s10492-016-0127-9
%G en
%F 10_1007_s10492_016_0127_9
Ngoc, Le Thi Phuong; Long, Nguyen Thanh. Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions. Applications of Mathematics, Tome 61 (2016) no. 2, pp. 165-196. doi: 10.1007/s10492-016-0127-9

Cité par Sources :