Related papers: On stabilization and control for the critical Klei…
We consider the Cauchy problem for systems of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution gains an additional…
We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies…
We consider a parametrically driven Klein--Gordon system describing micro- and nano-devices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear…
We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations…
Numerical simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime are performed. We use two structure-preserving discrete forms of the Klein--Gordon equation. The disparity between the two forms is the discretization…
It is classical that uniform stabilization of solutions to the autonomous damped wave equation is equivalent to every geodesic meeting the positive set of the damping, which is called the geometric control condition. In this paper, it is…
The goal for this paper is twofold. Our first main objective is to develop Bahouri-Gerard type profile decompositions for waves on hyperbolic space. Recently, such profile decompositions have proved to be a versatile tool in the study of…
We improve previous results on dispersive decay for 1D Klein- Gordon equation. We develop a novel approach, which allows us to establish the decay in more strong norms and weaken the assumption on the potential.
We extend the result M. Kowalczyk, Y. Martel, C. Mu\~noz, JEMS 2022, on the existence, in the context of spatially even solutions, of asymptotic stability on a center hypersurface at the soliton of the defocusing power Nonlinear Klein…
We study the Klein--Gordon equation $\Box\psi-\mu^2_{\textit{KG}}\psi=0$ on subextremal Kerr de Sitter black hole backgrounds with parameters $(a,M,l)$, where $l^2=\frac{3}{\Lambda}$. We prove a "relatively non degenerate integrated" decay…
We consider the strongly damped Klein Gordon equation for defocusing nonlinearity and we study the asymptotic behaviour of the energy for periodic solutions. We prove first the exponential decay to zero for zero mean solutions. Then, we…
We explore a new type of discretizations of lattice dynamical models of the Klein-Gordon type relevant to the existence and long-term mobility of nonlinear waves. The discretization is based on non-holonomic constraints and is shown to…
In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…
A generalization of classical cubic B-spline functions with a parameter is used as basis in the collocation method. Some initial boundary value problems constructed on the nonlinear Klein-gordon equation are solved by the proposed method…
The paper, classically, presents an extended Klein-Gordon field system in 3+1 dimensions with a special Q-ball solution. The Q-ball solution is energetically stable, that is, for any arbitrary small deformation above the background of that,…
We study nematic equilibria in an unbounded domain, with a two-dimensional regular polygonal hole with $K$ edges, in a reduced Landau-de Gennes framework. This complements our previous work on the "interior problem" for nematic equilibria…
In this paper, we study the numerical stabilization of a 1D system of two wave equations coupled by velocities with an internal, local control acting on only one equation. In the theoretical part of this study, we distinguished two cases.…
The nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit, namely as the speed of light $c$ tends to infinity, is considered. In particular, a higher-order normalized approximation of NLKG (which corresponds…
A spatially discrete version of the general kink-bearing nonlinear Klein-Gordon model in (1+1) dimensions is constructed which preserves the topological lower bound on kink energy. It is proved that, provided the lattice spacing h is…
We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…