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...

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...

A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP) formulated in the present work is the limit of the diffusion–reaction problem with a diffusion parameter tending to zero. To solve numerically the singularly perturbed diffusion– reaction problem, monotone approximations are employed. Numerical examples are presented f...

We construct a coupled set of nonlinear reaction-diffusion equations which are exactly solvable. The model generalizes both the Burger equation and a Boltzman reaction equation recently introduced by Th. W. Ruijgrok and T. T. Wu. Key-Words : non-linear dynamics, reaction-diffusion, solvable model. October 1993 CPT-93/P.2956 anonymous ftp or gopher: cpt.univ-mrs.fr ∗Bibos and Fakultät für Physik...

The general quasi-linear autonomous fourth order diffusion equation ut = −[G(u)uxxx + h(u, ux, uxx)]x with positive variable diffusivity G(u) and lower-order flux component h is considered on the real line. A direct algorithm produces a general class of equations for which the Shannon entropy density obeys a reaction-diffusion equation with a positive irreducible source term. Such equations may...