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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,...
∗The author was partially supported by Alexander von Humboldt Foundation and the Contract
MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.In this work we study the existence of global solution to
the semilinear wave equation (1.1) (∂2t − ∆)u = F(u),
where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace
operator on R^n.
The existence of solutions with small initial data, for the case of space dimensions
n = 3 was studied by F. John in [13],...
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