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In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a…
In this paper, we study the defocusing nonlinear Schr\"{o}dinger equation with a locally distributed damping on a smooth bounded domain as well as on the whole space and on an exterior domain. We first construct approximate solutions using…
In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We introduce a novel method to investigate the stability of wave packet dynamics under perturbations of the Hamiltonian. Our approach relies on semiclassical approximations, but is non-perturbative. Two separate contributions to the quantum…
The filamentation instability of the electromagnetic (EM) beam in an underdense plasma with high level of degeneracy is examined by means of the momentum equation, continuity equation and Maxwell's equations. It has been demonstrated that…
This study investigates a strongly-coupled system of partial differential equations (PDE) governing heat transfer in a copper rod, longitudinal vibrations, and total charge accumulation at electrodes within a magnetizable piezoelectric…
This paper is mainly concerned with the free boundary problem for an approximate model (for example, arising from the study of sonoluminescence) of a gas bubble of finite mass enclosed within a bounded incompressible viscous liquid,…
We consider the dynamic elasticity equation, modeled by the Euler-Bernoulli plate equation, with a locally distributed singular structural (or viscoelastic ) damping in a boundary domain. Using a frequency domain method combined, based on…
The electrostatic stability of electron-positron plasmas is investigated in the point-dipole and Z-pinch limits of dipole geometry. The kinetic dispersion relation for sub-bounce-frequency instabilities is derived and solved. For the…
In this paper, we investigate the stabilization of a locally coupled wave equations with local viscoelastic damping of past history type acting only in one equation via non smooth coefficients. First, using a general criteria of…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
When a polymer solution is uniaxially stretched and held fixed at both ends, the solution quickly separates into droplets connected by strings and takes the beads-on-string structure. The string then becomes thinner by capillary forces.…
In this paper, we analyze a semilinear damped second order evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. The nonlinear term satisfies a local Lipschitz continuity assumption. Under…
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of…
We prove the existence of strong time-periodic solutions and their asymptotic stability with the total energy of the perturbations decaying to zero at an exponential decay rate as $t \rightarrow \infty$ for a semilinear (nonlinearly…
We examine the stability of a 1D electrical transmission line in the simultaneous presence of PT-symmetry and fractionality. The array contains a binary gain/loss distribution $\gamma_{n}$ and a fractional Laplacian characterized by a…
The existence, uniqueness, and exponential stability results for mild solutions to the fractional neutral stochastic differential system are presented in this article. To demonstrate the results, the concept of bounded integral contractors…
We consider the phase transition of a string with tension $\eps_1$ to a string with a smaller tension $\eps_2$. The transition proceeds through quantum tunneling, and we calculate in arbitrary number of dimensions the pre-exponential factor…
In this paper we will study the asymptotic behaviour of the energy decay of a transmission plate equation with force and moment feedback. Precisly, we shall prove that the energy decay at least logarithmically over the time. The method…