Corrado Lattanzio

Global well-posedness and relaxation limits of a model for radiating gas

Abstract We study the initial value problem for a hyperbolic–elliptic coupled system with arbitrary large discontinuous initial data. We prove existence and uniqueness for that model by means of L1-contraction and comparison properties. Moreover, after suitable scalings, we study both the hyperbolic–parabolic and the hyperbolic–hyperbolic relaxation limits for that system.

Flocking and synchronization of particle models

In this note, we present a multi-dimensional flocking model rigorously derived from a vector oscillatory chain model and study the connection between the Cucker-Smale flocking model and the Kuramoto synchronization model appearing in the statistical mechanics of nonlinear oscillators. We provide an alternative direct approach for frequency synchronization to the Kuramoto model as an application of the flocking estimate for the Cucker-Smale model.

Convergence of a relaxation scheme for hyperbolic systems of conservation laws

Summary. This paper concerns the study of a relaxation scheme for

ON THE 3-D BIPOLAR ISENTROPIC EULER–POISSON MODEL FOR SEMICONDUCTORS AND THE DRIFT-DIFFUSION LIMIT

N\times N

Relative Entropy in Diffusive Relaxation

hyperbolic systems of conservation laws. In particular, with the compensated compactness techniques, we prove a rigorous result of convergence of the approximate solutions toward an entropy solution of the equilibrium system, as the relaxation time and the mesh size tend to zero.

HYPERBOLIC-PARABOLIC SINGULAR LIMITS FOR FIRST-ORDER NONLINEAR SYSTEMS

The aim of this paper is the study of the relaxation limit of the 3-D bipolar hydrodynamic model for semiconductors. We prove the convergence for the weak solutions to the bipolar Euler–Poisson system towards the solutions to the bipolar drifthyphen;diffusion system, as the relaxation time tends to zero.

Convergence of diffusive BGK approximations for nonlinear strongly parabolic systems

We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy. The relative entropy method is also employed to establish convergence from entropic weak solutions of viscoelasticity with memory to the system of viscoelasticity of the rate type.

The zero relaxation limit for 2×2 hyperbolic systems

Here W is the unknown n-vector function of (x, t) = (x1, . . . , xd , t) ∈ Rd × R+, Ā j = Ā j (W ) and A j = A j ( W ) (resp. Q = Q(W )) are smooth n × n-matrix (resp. n-vector) functions of W ∈ G (an open set in Rn), and W0(x ; ) is a given initial value function. For simplicity, we assume that Ā j , A j and Q do not depend on x, t and ; moreover, W0(x ; ) is periodic in x with period (1, . . . , 1) ∈ Rd (the same kind of results below holds also for other initial data like those with compact support).

Relative Energy for the Korteweg Theory and Related Hamiltonian Flows in Gas Dynamics

We study a class of BGK approximations of parabolic systems in one space dimension. We prove stability and existence of global solutions for this model. Moreover, under certain conditions, we prove a rigorous result of convergence toward the formal limit, by using compensated compactness techniques.

STABILITY OF SCALAR RADIATIVE SHOCK PROFILES

We study the zero relaxation limit for a class of 2 2 strictly hy-perbolic systems of balance laws. In particular we show the strong convergence toward the solution of the formal limit of the system and the validity of an innnite number of Kru zkov-type entropy inequalities. Moreover, we give a uniqueness result for this solution.