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Displaying 121 – 140 of 475

Exemples d’instabilités pour des équations d’ondes non linéaires

Guy Métivier (2002/2003)

Séminaire Bourbaki

Le but de l’exposé est de donner un guide de lecture pour un article de Gilles Lebeau où il est montré que le problème de Cauchy pour l’équation d’onde surcritique $(\partial_{t}^{2} - Δ_{x}) u + u^{p} = 0$ est mal posé au sens de Hadamard dans l’espace d’énergie, pour $p \geq 7$ en dimension 3. La preuve repose sur des constructions d’optique géométrique et des analyses d’instabilité dans des régimes fortement non linéaires. On donnera les étapes de l’analyse en essayant de les situer dans leur contexte plus général : construction de solutions...

Existence and asymptotic behaviour of solutions of a nonlinear evolution problem

Nelson Nery Oliveira Castro (1997)

Applications of Mathematics

We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for $\begin{matrix} u^{''} + A u - Δ u^{'} + {| v |}^{ρ + 2} {| u |}^{ρ} u = f_{1} \\ v^{''} + A v - Δ v^{'} + {| u |}^{ρ + 2} {| v |}^{ρ} v = f_{2} * \end{matrix}$ where $A$ is the pseudo-Laplacian operator.

Existence and asymptotic expansion of solutions to a nonlinear wave equation with a memory condition at the boundary.

Nguyen Thanh Long, Le Xuan Truong (2007)

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

Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Jong Yeoul Park, Sun Hye Park (2006)

Czechoslovak Mathematical Journal

We consider the damped semilinear viscoelastic wave equation $u^{''} - Δ u + \int_{0}^{t} h (t - τ) div {a \nabla u (τ)} d τ + g (u^{'}) = 0 in Ω \times (0, \infty)$ with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.

Existence and nonexistence results for reaction-diffusion equations in product of cones

Abdallah Hamidi, Gennady Laptev (2003)

Open Mathematics

Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.

Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation $u_{x t} = F (x, t, u, u_{x})$ .

Byszewski, L. (1990)

Journal of Applied Mathematics and Stochastic Analysis

Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms

Viorel Barbu, Irena Lasiecka, Mohammad Rammaha (2005)

Control and Cybernetics

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],...

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