Ricerc@Sapienza

Given A, Bin R^n imes n, we consider the Cauchy problem for partially dissipative hyperbolic systems having the form partiatl_t u+Apartial_x u+Bu = 0, with the aim of providing a detailed description of the large-time behavior. Sharp Lp-Lq estimates are established for the distance between the solution to the system and a time-asymptotic profile, where the profile includes a solution to a parabolic system and a solution of a hyperbolic system. The key tools for the proof are the Fourier transform together with the Young inequality and the interpolation inequality.

In this paper we study the mathematical model of the Goldbeter--Koshland switch, or
futile cycle, which is a mechanism that describes several chemical reactions, in particular the so-called
phosphorylation-dephosphorylation cycle. We determine the appropriate perturbation parameter epsilon
(related to the kinetic constants and initial conditions of the model) for the application of singular
perturbation techniques. We also determine the inner and outer solutions and the corresponding

We summarize some recent results concerning the study of the asymptotic properties of four important enzyme reactions, which are ubiquitous in every
intracellular enzyme reaction network. Mainly following the fundamental ideas by Nayfeh, after ad hoc adimensionalizations, we apply classical singular perturbation
techniques in order to determine the matched expansions of the solutions, in terms of a suitable parameter, up to the first order. We show some numerical results, for
the different mechanisms and different parameter values.

In this paper we study the mathematical model of auxiliary (or coupled) reactions, a mechanism
which describes several chemical reactions. In order to apply singular perturbation techniques, we determine
an appropriate perturbation parameter ǫ (which is related to the kinetic constants and initial conditions of the
model), the inner and outer solutions and the matched expansions of the solutions, up to the first order in ǫ, in
the total quasi-steady-state approximation (tQSSA) framework. The contribution of these expansions can be