相关论文: A stability analysis of a real space split operato…
In three dimensions, the parabolic-elliptic Keller-Segel system exhibits a rich variety of singularity formations. Notably, it admits an explicit self-similar blow-up solution whose radial stability, conjectured more than two decades ago in…
We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity \begin{equation*} \partial_{t}^{2}u-\partial_{x}^{2}u+u-|u|^{p-1}u+|u|^{q-1}u=0,\quad \mbox{on}\ [0,\infty)\times…
In this work, we consider the convergence analysis of time-splitting schemes for the nonlinear Klein--Gordon/wave equation under rough initial data. The optimal error bounds of the Lie splitting and the Strang splitting are established with…
We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with a nonlinear Klein-Gordon equation on a star graph. The proof of the well-posedness uses a classical fixed point…
We investigate the stability and stabilization of the cubic focusing Klein-Gordon equation around static solutions on the closed ball of radius L in $\mathbb{R}^3$. First we show that the system is linearly unstable near the static solution…
We consider the Klein-Gordon system posed in an inhomogeneous medium with smooth boundary subject to a local viscoelastic damping distributed around a neighborhoodof the boundary according to the Geometric Control Condition. We show that…
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…
Recently, finding exact solutions of nonlinear fractional differential equations has attracted great interest. In this paper, the space time-fractional Klein-Gordon equation with cubic nonlinearities is examined. Firstly, suitable exact…
The word stable is used to describe a situation when mathematical objects that almost satisfy an equation are close to objects satisfying it exactly. We study operator-algebraic forms of stability for unitary representations of groups and…
In the present work we examine the dynamics of a model for oscillons in 1-dimensional spacetime field theories with a cubic nonlinearity. We utilize a reduction of the model to first and third harmonics, which leads to a reduced partial…
We consider the problem of essential self-adjointness of the spatial part of the Klein-Gordon operator in stationary spacetimes. This operator is shown to be a Laplace-Beltrami type operator plus a potential. In globally hyperbolic…
We consider the problem of stability and approximability of Oseledets splittings and Lyapunov exponents for Perron-Frobenius operator cocycles associated to random dynamical systems. By developing a random version of the perturbation theory…
We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…
We consider the Klein--Gordon equation associated with the Laplace--Beltrami operator $\Delta$ on real hyperbolic spaces of dimension $n\!\ge\!2$; as $\Delta$ has a spectral gap, the wave equation is a particular case of our study. After a…
A method of ``algebraic estimates'' is developed, and used to study the stability properties of integrals of the form \int_B|f(z)|^{-\d}dV, under small deformations of the function f. The estimates are described in terms of a stratification…
In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the…
We consider a Strang-type second order operator-splitting discretization for the Cahn-Hilliard equation. We introduce a new theoretical framework and prove uniform energy stability of the numerical solution and persistence of all higher…
The present paper is a follow-up of our previous paper that derives a slightly simplified model equation for the Klein-Gordon equation, describing the propagation of a scalar field of mass $\mu$ in the background of a rotating black hole…
We study the stability of standing-waves solutions to a scalar non-linear Klein-Gordon equation in dimension one with a quadratic-cubic non-linearity. Orbits are obtained by applying the semigroup generated by the negative complex unit…
The Klein-Gordon equation in the Rindler space-time is studied carefully. It is shown that the stable properties depend on using what time coordinate to define the initial time. If we use the Rindler time, the scalar field is stable.…