We obtain free of resonances regions for the elasticity system in the exterior of a strictly convex body in R with dissipative boundary conditions under some natural assumptions on the behaviour of the geodesics on the boundary. To do so, we use the properties of the parametrix of the Neumann operator constructed in [12]. As a consequence, we obtain time decay estimates for the local energy of ...

A characterisation of the stochastic bounded generators of quantum irreversible Master equations is given. This suggests the general form of quantum stochastic evolution with respect to the Poisson (jumps), Wiener (diffusion) or general Quantum Noise. The corresponding irreversible Heisen-berg evolution in terms of stochastic completely positive (CP) maps is found and the general form of the st...

where: x is position in one or more spatial dimensions; u(x, t) is some scalar or vector field, such as fluid velocity and pressure; L is a dissipative linear operator, such as ∇; f(u) includes other autonomous terms representing nonlinear advection, reaction, etc.; and q(u, t) is some time dependent control or possibly stochastic forcing [22]. Among many physically relevant examples are Burger...

The conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a " reference " subharmonic operator bounded from below by the dissipative part of the infinitesimal generator. We discuss applications of this criteria in mathematical physics and quantum probability. 1. Introduction A quantum dynamical semigroup (q.d.s.) T = (T t) t≥0 on B(h), the Banach space of bound...

Owing to its lack of derivability, the dissipative anomaly operator appearing in the theory of turbulence without pressure recently proposed by Polyakov appears to be quite elusive. In particular, we give arguments that seem to lead to the conclusion that an anomaly in the first equation of the sequence of conservation laws cannot be a priori excluded. Permanent address: Center for Advanced Stu...

In this paper we analyze the transparency of the generalized scattering transformation applied to teleoperation systems with constant time delay. Particularly, the human operator, the remote environment, and the robot manipulators are modeled as dissipative instead of just passive systems. By the application of this transformation delay-independent stability is guaranteed. It is shown that tran...

This paper concerns the generation of a C0-semigroup by a streaming operator with general dissipative boundary conditions. Here, we give a third approach based on the construction of the generated semigroup without using the Hille-Yosida’s Theorem. The first approach, based on the HilleYosida’s Theorem, was given by Dautray [8], Protopopescu [9] and Voigt [10]. The second approach, based on the...

We consider here different models of dissipative Korteweg-de Vries (KdV) equations on the torus. Using a proper wave function Γ, we compare numerically the long time behavior effects of the damping models and we propose a hierarchy between these models. We also introduce a method based on the solution of an inverse problem to rebuild a posteriori the damping operator using only samples of the s...

We consider the dissipative singular q-Sturm-Liouville operators acting in Hilbert space L2 w,q(R+), that extensions of a minimal symmetric operator with deficiency indices (2, 2) (in limit-circle case).We construct self-adjoint dilation and its incoming outgoing spectral representations, which make it possible to determine scattering matrix terms Weyl-Titchmarsh function operator. also functio...

We employ a nonlinear anisotropic di usion operator like the ones used as a means of ltering and edge enhancement in image processing, in numerical methods for conservation laws. It turns out that algorithms currently used in image processing are very well suited for the design of nonlinear higher-order dissipative terms. In particular, we stabilize the well-known Lax-Wendro formula by means of...