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

Le Thi Phuong Ngoc, Nguyen Thanh Long (2016)

Applications of Mathematics

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,...

Existence in the Large for ... u = F (u) in Two Space Dimensions.

Robert T. Glassey (1981)

Mathematische Zeitschrift

Existence of absorbing set for a nonlinear wave equation.

Kurt, Ayfer (2002)

Applied Mathematics E-Notes [electronic only]

Existence of global solution of a nonlinear wave equation with short-range potential

V. Georgiev, K. Ianakiev (1992)

Banach Center Publications

Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in $3 + 1$ dimensions

Yvonne Choquet-Bruhat, Demetrios Christodoulou (1981)

Annales scientifiques de l'École Normale Supérieure

Existence of global solutions to a quasilinear wave equation with general nonlinear damping.

Aassila, Mohammed, Benaissa, Abbes (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of Global Solutions to Supercritical Semilinear Wave Equations

Georgiev, V. (1996)

Serdica Mathematical Journal

∗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],...