Bruno Rubino - Profile on Academia.edu (original) (raw)

Papers by Bruno Rubino

Asymptotic behavior of solutions to Euler–Poisson equations for bipolar hydrodynamic model of semiconductors

Journal of Differential Equations, 2013

ABSTRACT In this paper we study the Cauchy problem for 1-D Euler-Poisson system, which represents... more ABSTRACT In this paper we study the Cauchy problem for 1-D Euler-Poisson system, which represents a physically relevant hydrodynamic model but also a challenging case for a bipolar semiconductor device by considering two different pressure functions and a non-flat doping profile. Different from the previous studies (Gasser et al., 2003 [7], Huang et al., 2011 [12], Huang et al., 2012 [13]) for the case with two identical pressure functions and zero doping profile, we realize that the asymptotic profiles of this more physical model are their corresponding stationary waves (steady-state solutions) rather than the diffusion waves. Furthermore, we prove that, when the flow is fully subsonic, by means of a technical energy method with some new development, the smooth solutions of the system are unique, exist globally and time-algebraically converge to the corresponding stationary solutions. The optimal algebraic convergence rates are obtained.

Convergence of Approximate Solutions of the Cauchy Problem for a 2×2 Nonstrictly Hyperbolic System of Conservation Laws

Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects, 1993

NoDEA : Nonlinear Differential Equations and Applications, 1997

This paper regards the existence of weak solutions for a quasilinear wave equation of Klein-Gordo... more This paper regards the existence of weak solutions for a quasilinear wave equation of Klein-Gordon and Sine-Gordon type with the presence of a linear damping term and the relaxation to the reaction-diffusion equation when the momentum relaxation time tends to zero. In the limit process is fundamental the celebrated Div-curl Lemma of Tartar and Murat.

Journal of Mathematical Fluid Mechanics, 2005

This paper is devoted to study the asymptotic behaviors of the solutions to a model of hyperbolic... more This paper is devoted to study the asymptotic behaviors of the solutions to a model of hyperbolic balance laws with damping on the quarter plane (x, t) ∈ R + × R + . We show the optimal convergence rates of the solutions to their corresponding nonlinear diffusion waves, which are the solutions of the corresponding nonlinear parabolic equation given by the related Darcy's law. The optimal L p -rates (1 + t)

Convergence of the Fractional Step Method for a 2 × 2 Nonstrictly Hyperbolic System of Conservation Laws

Journal of Mathematical Analysis and Applications, 1996

We study the existence of solutions to the Cauchy problem for a non-homogeneous nonstrictly hyper... more We study the existence of solutions to the Cauchy problem for a non-homogeneous nonstrictly hyperbolic system of 2 × 2 conservation laws, satisfying the Lax entropy inequality. We obtain the convergence and the consistency of the approximating sequences generated by either the fractional Lax–Friedrichs or the fractional Godunov scheme. For this purpose we use the methods of the theory of

Porous media flow as the limit of a nonstrictly hyperbolic system of conservation laws

Communications in Partial Differential Equations, 1996

We show here that the weak solutions of the quasilinear hyperbolic system converge, as ∈ tends to... more We show here that the weak solutions of the quasilinear hyperbolic system converge, as ∈ tends to zero, to the solution of the reduced problem so that υ satisfies the nonlinear parabolic equation The limiting procedure is carried out by using the theory of compensated compactness. Finally we obtain the existence of Lyapounov functionals for the limit parabolic equation as

Kinetic and Related Models, 2012

In this paper we present a physically relevant hydrodynamic model for a bipolar semiconductor dev... more In this paper we present a physically relevant hydrodynamic model for a bipolar semiconductor device considering Ohmic conductor boundary conditions and a non-flat doping profile. For such an Euler-Poisson system, we prove, by means of a technical energy method, that the solutions are unique, exist globally and asymptotically converge to the corresponding stationary solutions. An exponential decay rate is also derived. Moreover we allow that the two pressure functions can be different.

Global existence to the Cauchy problem for hyperbolic conservation laws with an isolated umbilic point

Quarterly of Applied Mathematics, 2013

ABSTRACT The existence of global weak solutions for a 2×2 system of non-strictly hyperbolic nonli... more ABSTRACT The existence of global weak solutions for a 2×2 system of non-strictly hyperbolic nonlinear conservation laws is established for data in L ∞ . The result is proven by means of viscos approximation and application of the compensated compactness method. The presence of a degeneracy in the hyperbolicity of the system requires a careful analysis of the entropy functions, whose regularity is necessary to obtain an existence result. For the purpose we combine the classical techniques referring to a singular Euler-Poisson-Darboux equation with the compensated compactness method.

Journal of Non-Crystalline Solids, 2008

In this review, we study the Cauchy problem associated to the equation of linear and nonlinear vi... more In this review, we study the Cauchy problem associated to the equation of linear and nonlinear viscoelasticity with memory.Our first point is the study of dispersive properties of the solution to the linear equation of viscoelasticity with memory. The decay estimates obtained in this first part are important to treat the corresponding nonlinear Cauchy problem.The key novelty is the fact

Convergence to Traveling Waves with Decay Rates for Solutions of the Initial Boundary Problem to a Relaxation Model

Journal of Differential Equations, 1999

In this paper we consider a 2×2 relaxation hyperbolic system of conservation laws with a boundary... more In this paper we consider a 2×2 relaxation hyperbolic system of conservation laws with a boundary effect, and we show that the solutions of this initial boundary problem tend to the traveling wave solutions of the corresponding Cauchy problem time-asymptotically. In particular, we give the algebraic and exponential decay rates by using the weighted energy method. The location of a shift for the traveling wave, to overcome the difficulty in the boundary, plays a key role in this paper.

Journal of Differential Equations, 2000

In this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws... more In this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type. In particular we obtain a complete theory for the 2 2 systems of genuinely nonlinear hyperbolic balance laws in 1-D with a strong dissipative term. A di erent method, which combines the div-curl lemma with accretive operators, is then applied to study the limiting pro les in the case of nonhomogeneous isentropic gas dynamics. We also investigate relaxation results for some 2-D cases, which include the Cattaneo model for nonlinear heat conduction and the compressible Euler ow. Moreover, convergence result is also obtained for general semilinear systems in 1-D.

Archive for Rational Mechanics and Analysis, 2005

We treat the Cauchy problem for nonlinear system of viscoelasticity with memory term. We study th... more We treat the Cauchy problem for nonlinear system of viscoelasticity with memory term. We study the existence and time decay of the solution to this nonlinear problem. The kernel of the memory term includes integrable singularity at zero and polynomial decay at infinity. We prove the existence of a global solution for space dimensions n ≥ 3 and arbitrary quadratic nonlinearities.