By examining the Fourier transform of the initial datum near the origin, we define the decay character of the datum and provide a method to study the lower and upper algebraic rates of decay of solutions to a wide class of dissipative system of equations.

A loss of passivity in the face of certain frequency dynamics (eg: high frequency dynamics) given an otherwise passive system leads to the notion of a “mixed” system. A “mixed” system is one that has a concept of small gain associated with it over those frequency intervals where passivity is lost. In this paper, a test for determining “mixedness” for linear, time-invariant systems is provided a...

It is well known that a negative feedback interconnection of passive systems is passive. However, the extension of this fundamental property to the case of negative feedback interconnection of dissipative systems, which is a more general case, remains largely unaddressed. In this paper, we demonstrate that a negative feedback interconnection of dissipative systems, under appropriate assumptions...

In classical mechanics, Galilean covariance and the principle of relativity are completely equivalent and hold for all possible dynamical processes. In contrast, in relativistic physics the situation is much more complex. It will be shown that Lorentz covariance and the principle of relativity are not completely equivalent. The reason is that the principle of relativity actually only holds for ...

By introducing the notations of dissipative and strictly dissipative p-symmetrizers of initial-boundary-value problems for linear hyperbolic systems we formalize the dissipative integrals technique [A. Blokhin, Yu. Trakhinin, in Handbook of Mathematical Fluid Dynamics, Vol. 1, North-Holland, Amsterdam, 2002, pp. 545–652] applied earlier to shock waves and characteristic discontinuities for vari...