The simultaneous effect of amplification due to cooling and damping due to resonant absorption on the kink oscillations of coronal loops is studied. The governing equation describing the kink oscillations is derived in the thin tube thin boundary layer approximation. The cooling time is assumed to be much larger than the oscillation period, and the Wentzel-Kramers-Brillouin (WKB) method is used...

We obtain the nucleation rate of critical droplets for an elastic string moving in a phi(6) local potential and subject to noise and damping forces. The critical droplet is a bound soliton-antisoliton pair that carries a section of the string out of the metastable central minimum into one of the stable side minima. The frequencies of small oscillations about the critical droplet are obtained fr...

We present the theory of damping of low-energy excitations of a trapped Bose condensate at finite temperatures, where the damping is provided by the interaction of these excitations with the thermal excitations. We emphasize the key role of stochastization in the behavior of the thermal excitations for damping in non-spherical traps. The damping rates of the lowest excita-tions, following from ...

In this paper, we consider a coupled system of Petrovsky equations in a bounded domain with clamped boundary conditions. Due to several physical considerations, a linear damping which is distributed everywhere in the domain under consideration appears only in the first equation whereas no damping term is applied to the second one (this is indirect damping). Many studies show that the solution o...

The Ekman layer problem in a neutron star crust-core boundary is studied, taking into account possible slippage between the core flow (modelled as a single r-mode oscillation) and the crust, and allowing for a background magnetic field. With the help of a simple toy problem we derive basic estimates for the layer thickness and damping timescales, and show that the slippage enters linearly (inst...

In this paper, we study the logarithmic stability for the hyperbolic equations by arbitrary boundary observation. Based on Carleman estimate, we first prove an estimate of the resolvent operator of such equation. Then we prove the logarithmic stability estimate for the hyperbolic equations without any assumption on an observation sub-boundary.

We construct global L∞ entropy weak solutions to the initial boundary value problem for the damped compressible Euler equations on bounded domain with physical boundaries. Time asymptotically, the density is conjectured to satisfy the porous medium equation and the momentum obeys to the classical Darcy’s law. Based on entropy principle, we showed that the physical weak solutions converges to st...