This paper focuses on the anti-windup design for saturated 1-D linear reaction-diffusion equation which admits a finite number of unstable poles. We consider scenario in system is controlled via dynamic, finite-dimensional output feedback controller ensuring closed-loop exponential stability. A method proposed to dynamic compensator maximize region attraction and minimize effect external pertur...

The first considered problem is the problem of arising dynamic dissipative structures in the chemical reactor volume. The mathematical model of heat and mass transfer in the tubular through-reactors has been submitted. The model consists of the diffusion-kinetic equations for two reagents under the first-order reversible reaction and heat transfer equation with allowance for the latent heat of ...

Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps (∆x and ∆t) are varied independently. On the other hand, anisotropy effects due to the symmetries of the discretization lattice prevent the quantitative calibration of models. We introduce a new class of explicit difference methods for numeri...

We present Chapman–Enskog and Hilbert expansions applied to the O(v/c) Boltzmann equation for the radiative transfer of neutrinos in core-collapse supernovae. Based on the Legendre expansion of the scattering kernel for the collision integral truncated after the second term, we derive the diffusion limit for the Boltzmann equation by truncation of Chapman–Enskog or Hilbert expansions with react...