Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions

Le Thi Phuong Ngoc; Nguyen Thanh Long

Applications of Mathematics (2016)

  • Volume: 61, Issue: 2, page 165-196
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Ngoc, Le Thi Phuong, and Long, Nguyen Thanh. "Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions." Applications of Mathematics 61.2 (2016): 165-196. <http://eudml.org/doc/276793>.

@article{Ngoc2016,
abstract = {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.},
author = {Ngoc, Le Thi Phuong, Long, Nguyen Thanh},
journal = {Applications of Mathematics},
keywords = {nonlinear Love equation; Faedo-Galerkin method; local existence; blow up; exponential decay; nonlinear Love equation; Faedo-Galerkin method; local existence; blow up; exponential decay},
language = {eng},
number = {2},
pages = {165-196},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions},
url = {http://eudml.org/doc/276793},
volume = {61},
year = {2016},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 165
EP - 196
AB - 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.
LA - eng
KW - nonlinear Love equation; Faedo-Galerkin method; local existence; blow up; exponential decay; nonlinear Love equation; Faedo-Galerkin method; local existence; blow up; exponential decay
UR - http://eudml.org/doc/276793
ER -

References

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