In this article, we prove that the Kolmogorov operator associated to the Burgers equation driven by a space-time white noise is m-dissipative. This implies several properties on the Kolmogorov equation. This result is obtained thanks to the introduction of a modified Kolmogorov operator. New a priori estimates on the solutions of the Burgers equation and on the invariant measure are obtained. T...

A bstract Inspired by the universal operator growth hypothesis, we extend formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our is based upon modification Liouvillian superoperator appropriate Lindbladian, thereby following vectorized Lanczos algorithm and Arnoldi iteration. This well justified due incorporation non-Hermitian effects environment...

<p style='text-indent:20px;'>In this paper, we develop a natural operator-splitting variational scheme for general class of non-local, degenerate conservative-dissipative evolutionary equations. The splitting-scheme consists two phases: conservative (transport) phase and dissipative (diffusion) phase. first is solved exactly using the method characteristic DiPerna-Lions theory while secon...

This paper addresses the problem of following an arbitrary path with a dissipative passive haptic display. Such a display has energetically passive actuators; all motive energy must come initially from the human operator and the display may then in general dissipate, redirect, and/or store the energy. Due to the passive restriction conventional haptic control techniques are not applicable. Thre...

We study the wave equation in exterior of a bounded domain K with dissipative boundary condition $$\partial _{\nu } u - \gamma (x) \partial _t = 0$$ on $$\Gamma $$ and $$\gamma > 0.$$ The solutions are described by contraction semi-group $$V(t) e^{tG}, \, t \ge eigenvalues $$\lambda _k$$ G $$\text{ Re }\,\lambda _k < yield asymptotically disappearing $$u(t, x) e^{\lambda t} f(x)$$ having expone...

Given a dissipative operator \(A\) on complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) is closable, we give necessary and sufficient condition for an extension of to still be dissipative. As applications, describe all maximally accretive extensions strictly positive symmetric operators highly singular first-order interval.