相关论文: Existence and stability of periodic planar standin…
This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…
The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of periodic traveling wave solutions implies their orbital…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
The purpose of this paper is to investigate the stabilization of a one-dimensional coupled wave equations with non smooth localized viscoelastic damping of Kelvin-Voigt type and localized time delay. Using a general criteria of…
We analyze the distortion of wind-generated near-inertial waves by steady and unsteady barotropic quasi-geostrophic eddies, with a focus on the evolution of the horizontal wavevector $\boldsymbol{k}$ under the effects of mesoscale strain…
Recently there has been interest in studying a new class of elastic materials, which is described by implicit constitutive relations. Under some basic assumption for elasticity constants, the system of governing equations of motion for this…
We consider the transition from a spatially uniform state to a steady, spatially-periodic pattern in a partial differential equation describing long-wavelength convection. This both extends existing work on the study of rolls, squares and…
We present a phenomenological time-dependent Ginzburg-Landau theory of nonlinear plastic deformations in solids. Because the problem is very complex, we first give models in one and two dimensions without vacancies and interstitials, where…
We consider existence and stability properties of nonlinear spatially periodic or quasiperiodic standing waves (SWs) in one-dimensional lattices of coupled anharmonic oscillators. Specifically, we consider Klein-Gordon (KG) chains with…
A coupled system composed of a Newtonian fluid located on a sinusoidally-forced elastic solid is studied analytically and numerically. The focus is on the transient evolution from the beginning of the forced oscillations and on the periodic…
In this paper we investigate the existence of solutions in $H^1(R^N) \times H^1(R^N)$ for nonlinear Schr\"odinger systems of the form \[ \left\{ \begin{aligned} -\Delta u_1 &= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + r_1\beta…
We provide a detailed study of the dynamics obtained by linearizing the Korteweg-de Vries equation about one of its periodic traveling waves, a cnoidal wave. In a suitable sense, linearly analogous to space-modulated stability, we prove…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
This paper presents an electromechanical analysis of the nonlinear static response and the superimposed small-amplitude wave characteristics in an infinite periodic compressible dielectric elastomer (DE) laminate subjected to electrostatic…
We study the evolution of nonlinear surface gravity water-wave packets developing from modulational instability over an uneven bottom. A nonlinear Schr\"odinger equation (NLSE) with coefficients varying in space along propagation is used as…
It is well-known that the rarefaction wave, one of the basic wave patterns to the hyperbolic conservation laws, is nonlinearly stable to the one-dimensional compressible Navier-Stokes equations (cf. [14,15,12,17]). In the present paper we…
We study the linear stability of Plane Poiseuille flow of an elastoviscoplastic fluid using a revised version of the model proposed by Putz and Burghelea (Rheol. Acta (2009)48:673-689). The evolution of the microstructure upon a gradual…
We investigate the stabilization of a locally coupled wave equations with only one internal viscoelastic damping of Kelvin-Voigt type. The main novelty in this paper is that both the damping and the coupling coefficients are non smooth.…
In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear non-modal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the non-trivial time evolution of non-modal…