Related papers: A stability criterion for high-frequency oscillati…
In this paper we study global nonlinear stability for a system of semilinear wave and Klein-Gordon equations with quadratic nonlinearities. We consider nonlinearities of the type of wave-Klein-Gordon interactions where there are no…
We are interested in establishing stability results for a system of semilinear wave and Klein-Gordon equations with mixed coupling nonlinearities, that is, we consider all of the possible quadratic nonlinear terms of the type of wave and…
A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear…
This work intends to prove that strong instabilities may appear for high order geometric optics expansions of weakly stable quasilinear hyperbolic boundary value problems, when the forcing boundary term is perturbed by a small amplitude…
We study the ``hyperboloidal Cauchy problem'' for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behaviour at the boundary, or with polyhomogeneous initial data.…
We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions…
A stability criterion is derived for self-similar solutions with perfect fluids which obey the equation of state $P=k\rho$ in general relativity. A wide class of self-similar solutions turn out to be unstable against the so-called kink…
Multistability -- the emergence of multiple stable states under identical conditions -- is a hallmark of nonlinear complexity and an enabling mechanism for multilevel optical memory and photonic computing. Its realization in a compact…
We consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the classical solution under a new structural condition…
This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…
In this note we provide some precise estimates explaining the diffusive structure of partially dissipative systems with time-dependent coefficients satisfying a uniform Kalman rank condition. Precisely, we show that under certain (natural)…
Solutions of the system of evolutionary equations in the short-wavelength approximation are found and studied. A connection is established between the problem of the evolution of short-wavelength gravitational-scalar perturbations and the…
The generation of large-amplitude coherent states of a massive mechanical resonator, and their quantum-limited detection represent useful tools for quantum sensing and for testing fundamental physics theories. In fact, any weak perturbation…
We study the weakly stable hyperbolic boundary value problem with a large zero order oscillatory coefficient. This problem is related to linearized problems in the study of Mach stem and vortex sheets. We wish to establish a uniform energy…
We study general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. These coefficients are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are…
Given small initial solutions of the nonlinear quantum harmonic oscillator on $\mathbb{R}$, we are interested in their long time behavior in the energy space which is an adapted Sobolev space. We perturbate the linear part by $V$ taken as…
This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for each $t, x$ the principal symbol is hyperbolic. No hypothesis…
We consider a chain of $n$ coupled oscillators placed on a one-dimensional lattice with periodic boundary conditions. The interaction between particles is determined by a weakly anharmonic potential $V_n = r^2/2 + \sigma_nU(r)$, where $U$…
A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…
A mesoscopic model of a diblock copolymer is used to study the stability of a uniform lamellar phase under a reciprocating shear flow. Approximate viscosity contrast between the microphases is allowed through a linear dependence of the…