Geometrical interpretation of the sinh-Gordon equation
Géométrie des systèmes hyperboliques de lois de conservation
Geometry of stationary sets for the wave equation in . The case of finitely supported initial data: An announcement.
Gerbes singulières et singularités du problème de Cauchy hyperbolique
Global attractor for the perturbed viscous Cahn-Hilliard equation
We consider the initial-boundary value problem for the perturbed viscous Cahn-Hilliard equation in space dimension n ≤ 3. Applying semigroup theory, we formulate this problem as an abstract evolutionary equation with a sectorial operator in the main part. We show that the semigroup generated by this problem admits a global attractor in the phase space (H²(Ω)∩ H¹₀(Ω)) × L²(Ω) and characterize its structure.
Global attractor of the Cauchy problem for a semilinear degenerate damped hyperbolic equation involving the Grushin operator
The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate damped hyperbolic equation involving the Grushin operator with a locally Lipschitz nonlinearity satisfying a subcritical growth condition.
Global boundary controllability of the de St. Venant equations between steady states
Global Classical Solutions of Nonlinear Wave Equations.
Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems
In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a solution and its stability with certain small initial and boundary data.
Global classical solutions to the Cauchy problem for a nonlinear wave equation.
Global dynamics beyond the ground state energy for nonlinear dispersive equations
This is a brief introduction to the joint work with Wilhelm Schlag and Joachim Krieger on the global dynamics for nonlinear dispersive equations with unstable ground states. We prove that the center-stable and the center-unstable manifolds of the ground state solitons separate the energy space by the dynamical property into the scattering and the blow-up regions, respectively in positive time and in negative time. The transverse intersection of the two manifolds yields nine sets of global dynamics,...
Global existence and asymptotic behavior of solutions for a class of nonlinear degenerate wave equations.
Global existence and asymptotic behavior of solutions for some nonlinear hyperbolic equation.
Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions.
Global existence and energy decay of solutions to a Bresse system with delay terms
We consider the Bresse system in bounded domain with delay terms in the internal feedbacks and prove the global existence of its solutions in Sobolev spaces by means of semigroup theory under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method.
Global existence and energy decay of solutions to the Cauchy problem for a wave equation with a weakly nonlinear dissipation.
Global existence and internal nonlinear stabilization of an elasticity system. (Existence globale et stabilisation interne non linéaire d'un système d'élasticité.)
Global existence and nonlinear boundary stabilization of an elastic system. (Existence globale et stabilisation frontière non linéaire d'un système d'élasticité.)
Global existence and polynomial decay for a problem with Balakrishnan-Taylor damping
A viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping is considered. Using integral inequalities and multiplier techniques we establish polynomial decay estimates for the energy of the problem. The results obtained in this paper extend previous results by Tatar and Zaraï [25].
Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents
We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms We prove with suitable assumptions on the variable exponents the global existence...