This paper is devoted to moment exponential stability of a class Markovian switching stochastic differential equations with impulsive perturbations. Taking into consideration the long time behavior device, we derive explicit criteria for and instability. The contribution perturbations instability revealed.

We study the Turing instability to stationary spatial patterns in reaction-transport systems with inertia. After a brief discussion of hyperbolic reaction-diffusion equations and reaction-Cattaneo equations we focus on reaction randomwalks, which are themost natural generalization of reactiondiffusion equations. We analyze the effect of inertia in the transport on spatial instabilities of the h...

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.

The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatiblewith the constraint equations inadvertently leads to ‘constraint violatingmodes’ propagating into the computational domain from the boundary. The other source for constraint violation is...

In the article, a differential scheme is created for first-order diffusion equation using Crank-Nicolson method. The stability of was checked Neumann To solve problem numerically, intervals were found Neman This work presents an analysis two-dimensional Von analysis. widely used numerical method solving partial equations that combines explicit and implicit schemes. important factor to consider ...

The role of topology in the perturbative solution of the Euclidean Einstein equations (EEEs) about flat instantons is examined. When the topology is open (with asymptotically flat boundary conditions) it is simple to demonstrate that all vacuum perturbations vanish at all orders in perturbation theory; when the topology is closed (a four-torus say) all but a 10-parameter family of global metric...

In order to study the growth of heterogeneity in granular systems, we investigate the quasi-static deformation of monodisperse particle systems with regular initial arrangements. We construct a linearized model by limiting our consideration to infinitesimal deformations. Assuming Coulomb friction, we introduce new variables to express the slippage distances of particles in contact. The results ...

We study here instability problems of standing waves for the nonlinear Klein-Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave’s frequency or the wave’s speed of propagation and on the nonlinearity.

At very high radiation field intensities in vacuum, Maxwell equations need to be modified to account for the QED photon-photon interaction. We show that such modified equations support nondiffracting spatial radiation solitons that propagate for very long distances without changing their shapes. These solitons, and the underlying self-focusing and instability effects, should be observable in th...