Trend to equilibrium for systems with small cross-diffusion

Trend to Equilibrium for Reaction-Diffusion Systems Arising from Complex Balanced Chemical Reaction Networks

The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper, by deriving explicitly the entropy dissipation, we show that for complex balanced systems without boundary equilibria, each trajectory converges exponentiall...

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

On the Trend to Equilibrium for Some Dissipative Systems with Slowly Increasing a Priori Bounds

We prove convergence to equilibrium with explicit rates for various kinetic equations with relatively bad control of the distribution tails : in particular, Boltzmann-type equations with (smoothed) soft potentials. We compensate the lack of uniform in time estimates by the use of precise logarithmic Sobolevtype inequalities, and the assumption that the initial datum decays rapidly at large velo...

Exit asymptotics for small diffusion about an unstable equilibrium

A dynamical system perturbed by white noise in a neighborhood of an unstable fixed point is considered. We obtain the exit asymptotics in the limit of vanishing noise intensity. This is a refinement of a result by Kifer (1981).

On the Trend to Global Equilibrium for Spatially Inhomogeneous Kinetic Systems: the Boltzmann Equation