MATHEMATICAL MODELLING FOR SEMICONDUCTOR DEVICES

Mathematical problems in semiconductor physics.   Edited by P. Marcati, P. A. Markowich and R. Natalini. Pitman Research Notes in Mathematics Series, 340. Longman, Harlow, 1995. vi+214 pp. ISBN: 0-582-28704-9 82-06 (00B25 78-06)

Hailiang Li, Marcati, Pierangelo;  Existence  and asymptotic behavior of multi-dimensional quantum hydrodynamical model for semiconductors,  Comm. Math. Phys.  245  (2004),  no. 2, 215--247. 

Gasser, Ingenuin; Marcati, Pierangelo;  A quasi-neutral limit in the hydrodynamic model for charged fluids. Monatsh. Math. 138 (2003),189--208.

Gasser, Ingenuin, Marcati, Pierangelo; A Vanishing Debye Length Limit in Hydrodynamic Model for  Semiconductors, Hyperbolic problems: theory, numerics, applications:  Eighth international conference in Magdeburg, February, March 2000, ed. by H. Freist\"uhler and  G. Warnecke, Birkh\"auser, Basel, 409--414 (2001)

Gasser, Ingenuin, Marcati, Pierangelo; A Vanishing Debye Length Limit in Hydrodynamic Model for  Semiconductors, Hyperbolic problems: theory, numerics, applications:  Eighth international conference in Magdeburg, February, March 2000, ed. by H. Freist\"uhler and  G. Warnecke, Birkh\"auser, Basel, 409--414 (2001)

Lattanzio, Corrado; Marcati, Pierangelo; The relaxation to the drift-diffusion system for the 3-D isentropic Euler-Poisson model for semiconductors. Discrete Contin. Dynam. Systems 5 (1999), no. 2, 449--455.

Marcati, P. A.; Natalini, R. Relaxation phenomena for the hydrodynamic models in semiconductors.
Mathematical problems in semiconductor physics (Rome, 1993), 153--164, Pitman Res. Notes Math. Ser., 340, Longman, Harlow, 1995.
 
Marcati, Pierangelo; Natalini, Roberto; Entropy solutions for a hydrodynamic model for semiconductors.
Nonlinear evolutionary partial differential equations (Beijing, 1993), 311--317, AMS/IP Stud. Adv. Math., 3, Amer. Math. Soc., Providence, RI, 1997.

Ali' Giuseppe; Marcati, Pierangelo; Natalini, Roberto;  Hydrodynamical models for semiconductors. Z. Angew. Math. Mech. 76, Suppl. 2, 301-304 (1996)
 
Marcati, Pierangelo; Natalini, Roberto Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation Arch. Rational Mech. Anal. 129 (1995), no. 2, 129--145.

Marcati, Pierangelo; Natalini, Roberto Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), no. 1, 115--131



HYPERBOLIC SYSTEMS, DIFFUSIVE LIMITS, NONLINEAR WAVES

Hyperbolic Systems of Conservation Laws.  A.BRESSAN, D.SERRE, M.WILLIAMS, K.ZUMBRUN, Editor: P.MARCATI,  Lecture Notes in Mathematics, (vol. LNM 1911 - CIME Serie). ISBN: 978-3-540-72186-4. HEIDELBERG: Springer-Verlag, 2007.  

Donatelli, Donatella; Marcati, Pierangelo  Convergence of singular limits for multi-D semilinear hyperbolic systems to parabolic systems. Trans. Amer. Math. Soc. 356 (2004), no. 5, 2093--2121

Donatelli, Donatella; Marcati, Pierangelo;  Singular limits for nonlinear hyperbolic systems   Progress in Nonlinear differential equations and their applications, Birkhauser, Basel, 50(2002)79-96

Donatelli, Donatella; Marcati, Pierangelo Parabolic Relaxation of semilinear Multidimensional Hyperbolic Systems, Hyperbolic problems: theory, numerics, applications:  Eighth international conference in Magdeburg, February, March 2000, ed. by H. Freist\"uhler and  G. Warnecke, Birkh\"auser, Basel, 307-316 (2001).

Marcati Pierangelo;  Rubino Bruno;  Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems, J.Differential Equations 162 (2000), no.2, 359--399.

Donatelli, Donatella; Marcati, Pierangelo;  Relaxation of semilinear hyperbolic systems with variable coefficients.  Ric. Mat. 48, Suppl., 295-310 (1999).

Marcati, Pierangelo; Rubino, Bruno; Hyperbolic to parabolic relaxation for quasilinear first order systems in several space dimensions.
Proceedings of the IX International Conference on Waves and Stability in Continuous Media (Bari, 1997). Rend. Circ. Mat. Palermo (2) Suppl. 1998, no. 57, 315--320.

Lattanzio, Corrado; Marcati, Pierangelo; The zero relaxation limit for $2\times2$ hyperbolic systems. Nonlinear Anal. 38 (1999), no. 3, Ser. A: Theory Methods, 375--389.
 
Marcati, Pierangelo; Rubino, Bruno; Entropy methods for nonstrictly hyperbolic systems. J. Partial Differential Equations 10 (1997), no. 4, 333--346.
 
Marcati, Pierangelo; Natalini, Roberto; Global weak entropy solutions to quasilinear wave equations of Klein-Gordon and sine-Gordon type. J. Math. Soc. Japan 50 (1998), no. 2, 433--449.

Lattanzio, Corrado; Marcati, Pierangelo; The zero relaxation limit for the hydrodynamic Whitham traffic flow model. J. Differential Equations 141 (1997), no. 1, 150--178.

Marcati, Pierangelo; Milani, Albert The one-dimensional Darcy's law as the limit of a compressible Euler flow. J. Differential Equations 84 (1990), no. 1, 129--147.
 
Marcati, Pierangelo; Milani, Albert J.; Secchi, Paolo Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system. Manuscripta Math. 60 (1988), no. 1, 49--69.


QUANTUM FLUIDS

Antonelli Paolo, Marcati Pierangelo;  On the finite energy weak solutions to a system in quantum fluid dynamics  -   preprint

Hailiang Li, Marcati, Pierangelo;  Existence  and asymptotic behavior of multi-dimensional quantum hydrodynamical model for semiconductors,  Comm. Math. Phys.  245  (2004),  no. 2, 215--247. 


CLASSICAL FLUIDS and FLUID MODELS

Donatelli, Donatella; Marcati, Pierangelo,  A dispersive approach to the artificial compressibility approximations of the Navier Sokes equations in 3-D.   Jou. Hyp. Differential Equations  J. Hyperbolic Differ. Equ. 3 (2006), 575-588.

Huang Feimin, Marcati Pierangelo, Pan Ronghua,   Convergence to Barenblatt solution for the compressible Euler equations with damping and vacuum, Arch. Ration. Mech. Anal. 176 (2005), 1-24.
 
Marcati Pierangelo, Mei Ming, Rubino Bruno Optimal Convergence Rates to Diffusion Waves for Solutions of the Hyperbolic Conservation Laws with Damping, J. Math. Fluid Mech.7, Suppl. 2, S224-S240 (2005)
 
Lattanzio, Corrado; Marcati, Pierangelo; Global well-posedness and relaxation limits of a model for radiating gas. J. Differential Equations 190 (2003),  439--465

Di Francesco, Marco; Marcati, Pierangelo;  Singular convergence to nonlinear diffusion waves for solutions to the Cauchy problem for the compressible Euler equations with damping.  Math. Models Methods Appl. Sci.  12  (2002),  no. 9, 1317--1336.

Marcati, Pierangelo, Pan, Ronghua; On the diffusive profiles for the system of compressible adiabatic flow through porous media. SIAM J. Math. Anal. 33 (2001).

Marcati, Pierangelo; Pan, Ronghua    Cauchy problem for compressible Euler equations with damping. Fiedler, B. (ed.) et al., International conference on differential equations.   Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1-7, 1999. Vol. 1. Singapore: World Scientific. 315-317 (2000).

Marcati, Pierangelo; Milani, Albert Fluid flow in macromolecular systems and related perturbation problems. Ann. Fac. Sci. Toulouse Math. (5) 11 (1990), no. 3, 73--92.
 
Marcati, Pierangelo; Milani, Albert The one-dimensional Darcy's law as the limit of a compressible Euler flow. J. Differential Equations 84 (1990), no. 1, 129--147.