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.

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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.
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 
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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. http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0127-9/

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