Pierangelo Marcati

Full Professor

Coppito 1, Room
pierangelo.marcati@univaq.it
+39(086)2433143

Quantum hydrodynamics

Classical and Nonclassical fluids

Mathematical models in Engineering and Biology

 

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Research Papers

74- D. Donatelli and P. Marcati. Quasineutral limit for the Navier Stokes Fourier Poisson System in plasma physics, Springer Proceedings in Mathematics & Statistics, 49, (2013), 193-206

73- Di Michele Federica; Marcati, Pierangelo; Rubino, Bruno; A physical derivation of boundary conditions for the quantum hydrodynamic system (submitted)

72- Donatelli, Donatella; Marcati, Pierangelo;  Analysis of oscillations and defect measures for the quasineutral limit in plasma physics. Arch. of Rat. Mech. and Analysis, 206, no. 1, (2012), 159-188

71- Donatelli, Donatella; Marcati, Pierangelo; Low Mach Number Limit on Exterior Domains; to appear Acta Mathematica Scientia, 2011.

70- Antonelli, Paolo; Marcati, Pierangelo; The Quantum Hydrodynamics System in Two Space Dimensions Arch. Ration. Mech. Anal. (2011) DOI: 10.1007/s0020501104547

69- Di Michele Federica; Marcati, Pierangelo; Rubino, Bruno; Steady states and interface transmission conditions for heterogeneous quantumclassical 1D hydrodynamic model of semiconductor devices (submitted)

68 Donatelli, Donatella; Marcati, Pierangelo; Leray weak solutions of the incompressible Navier Stokes system on exterior domains via the artificial compressibility method. Indiana Univ. Math. J. 59 (2010), 1831—1852.

67- Antonelli, Paolo; Marcati, Pierangelo; On the finite energy weak solutions to a system in Quantum Fluid Dynamics, Comm. Math. Phys. 287 (2009) 657686.

67- Antonelli, Paolo; Marcati, Pierangelo;   On the finite energy weak solutions to a system in Quantum Fluid Dynamics, to appear Comm. Math. Phys. 2008

66- Donatelli, Donatella; Marcati, Pierangelo; Artificial compressibility approximation for the incompressible Navier-Stokes equations on unbounded domain.  Benzoni-Gavage, Sylvie (ed.) et al., Hyperbolic problems. Theory, numerics and applications. Berlin: Springer. (2008) 475-483.

65- Donatelli, Donatella; Marcati, Pierangelo;  A quasineutral type limit for the Navier–Stokes–Poisson system with large data, Nonlinearity 21 (2008) 135–148

64- Gasser Ingenuin, Marcati Pierangelo;  On a Generalisation of the ``Div-Curl Lemma'', to appear in Osaka Journal of Mathematics, vol. 45 (1), (2008).

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

 

62- 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.
 
61- 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)
 
60- 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
 
59- 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. 
 
58- Marcati, Pierangelo; Nishihara, Kenji;   The Lp-Lq  estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media. J. Differential Equations 191 (2003), 445--469.
 
57- Lattanzio, Corrado; Marcati, Pierangelo; Global well-posedness and relaxation limits of a model for radiating gas. J. Differential Equations 190 (2003),  439--465.
 
56- 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.
 
55- Gasser, Ingenuin; Marcati, Pierangelo;  A quasi-neutral limit in the hydrodynamic model for charged fluids. Monatsh. Math. 138 (2003),189--208.
 
54- Donatelli, Donatella; Marcati, Pierangelo;  Singular limits for nonlinear hyperbolic systems   Progress in Nonlinear differential equations and their applications, Birkhauser, Basel, 50(2002)79-96

53- Marcati, Pierangelo, Pan, Ronghua; On the diffusive profiles for the system of compressible adiabatic flow through porous media. SIAM J. Math. Anal. 33 (2001).
 
52- 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).
 
51- Gasser, Ingenuin, Marcati, Pierangelo   The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductors   Math. Methods Appl. Sci.24 (2001) 81-92.
 
50- 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).
 
49- 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).
 
48- Marcati, Pierangelo; Mei, Ming; Convergence to nonlinear diffusion waves for solutions of the initial boundary problem to the hyperbolic conservation  laws with damping. Quart. Appl. Math. 58 (2000), no. 4, 763--784.
 
47- Donatelli, Donatella; Marcati, Pierangelo;  1-D relaxation from Hyperbolic to Parabolic Systems with Variable Coefficients,  Rend. Ist. Mat. Univ. Trieste Suppl. Vol. XXXI, 63-85 (2000)
 
46- Marcati Pierangelo;  Rubino Bruno;  Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems, J.Differential Equations 162 (2000), no.2, 359--399.
 
45- Lattanzio, Corrado; Marcati, Pierangelo; Asymptotic stability of plane diffusion waves for the 2-D quasilinear wave equation. Contemp. Math., 238, 163--182, Amer. Math. Soc., Providence, RI, 1999.
 
44- Donatelli, Donatella; Marcati, Pierangelo;  Relaxation of semilinear hyperbolic systems with variable coefficients.  Ric. Mat. 48, Suppl., 295-310 (1999).
 
43- 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.
 
42- Lattanzio, Corrado; Marcati, Pierangelo; Diffusive profile for the 2-D nonlinear damped wave equation.
Proceedings of the IX International Conference on Waves and Stability in Continuous Media (Bari, 1997). Rend. Circ. Mat. Palermo (2) Suppl. 1998, no. 57, 293--302.
 
41- Lattanzio, Corrado; Marcati, Pierangelo; The zero relaxation limit for times2$ hyperbolic systems. Nonlinear Anal. 38 (1999), no. 3, Ser. A: Theory Methods, 375--389.
 
40- Marcati, Pierangelo; Molinari, Manuela; Evolution of hypersurfaces in ${R}sp N$ by Gaussian curvature. NoDEA Nonlinear Differential Equations Appl. 6 (1999), no. 2, 119--132.
 
39- 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.
 
38- Marcati, Pierangelo; Rubino, Bruno; Entropy methods for nonstrictly hyperbolic systems. J. Partial Differential Equations 10 (1997), no. 4, 333--346.
 
37- 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.
 
36- Lattanzio, Corrado; Marcati, Pierangelo; The zero relaxation limit for the hydrodynamic Whitham traffic flow model. J. Differential Equations 141 (1997), no. 1, 150--178.
 
35- Marcati, Pierangelo; Rubino, Bruno Parabolic relaxation limit for hyperbolic systems of conservation laws.  Proceedings of the VIII International Conference on Waves and Stability in Continuous Media, Part I (Palermo, 1995). Rend. Circ. Mat. Palermo (2) Suppl. No. 45, part I , (1996), 393--406.
 
34- 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.
 
33- 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.
 
32- Ali' Giuseppe; Marcati, Pierangelo; Natalini, Roberto;  Hydrodynamical models for semiconductors. Z. Angew. Math. Mech. 76, Suppl. 2, 301-304 (1996)
 
31- Marcati, Pierangelo; Natalini, Roberto; On the hydrodynamic model for semiconductors and the relaxation to the drift-diffusion equation.
Hyperbolic problems: theory, numerics, applications (Stony Brook, NY, 1994), 198--206, World Sci. Publishing, River Edge, NJ, 1996
 
30- Marcati, Pierangelo Weak solutions to a nonlinear partial differential equation of mixed type. Differential Integral Equations 9 (1996), no. 4, 827--848.
 
29- Marcati, Pierangelo; Rubino, Bruno History-dependent scalar conservation laws. Rend. Sem. Mat. Univ. Padova 96 (1996), 195--204.
 
28- 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.
 
27- 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
 
26- Marcati, Pierangelo; Natalini, Roberto; Convergence of the pseudo-viscosity approximation for conservation laws. Nonlinear Anal. 23 (1994), no. 5, 621--628.
 
25- Esteban, Juan R.; Marcati, Pierangelo; Approximate solutions to first and second order quasilinear evolution equations via nonlinear viscosity. Trans. Amer. Math. Soc. 342 (1994), no. 2, 501--521
 
24- 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.
 
23- 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.
 
22- Marcati, Pierangelo Convergence of approximate solutions to scalar conservation laws by degenerate diffusion. Rend. Sem. Mat. Univ. Padova 81 (1989), 65--78.
 
21- Hsiao, Ling; Marcati, Pierangelo; Nonhomogeneous quasilinear hyperbolic system arising in chemical engineering. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), no. 1, 65--97 (1989).
 
20- Marcati, Pierangelo Nonhomogeneous quasilinear hyperbolic systems: initial and boundary value problems. Calculus of variations and partial differential equations (Trento, 1986), 193--200,   Lecture Notes in Math., 1340, Springer, Berlin-New York, 1988.
 
19- Marcati, P. A result on hyperbolic aspects in the theory of porous media. Boll. Un. Mat. Ital. A (7) 3 (1989), no. 1, 69--75.
 
18- Marcati, Pierangelo Relaxation for Nonlinear Hyperbolic Systems  Proceedings  Prima Reunion Italia Espana de Analys Nolineal   (L. Boccardo ed.) El Escorial 1989
 
17- 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.
 
16- Marcati, Pierangelo; Approximate solutions to conservation laws via convective parabolic equations: analytical and numerical results.
Dynamics of infinite-dimensional systems (Lisbon, 1986), 169--177, NATO Adv. Sci. Inst. Ser. F: Comput. Systems Sci., 37, Springer, Berlin-New York, 1987.
 
15- Marcati, Pierangelo; Approximate solutions to conservation laws via convective parabolic equations. Comm. Partial Differential Equations 13 (1988), no. 3, 321--344.
 
14- Marcati, Pierangelo; Approximate solutions to scalar conservation laws via degenerate diffusion. Hyperbolic equations (Padua, 1985), 272--277, Pitman Res. Notes Math. Ser., 158, Longman Sci. Tech., Harlow, 1987.
 
13- Marcati, Pierangelo Abstract stability theory and applications to hyperbolic equations with time dependent dissipative force fields. Hyperbolic partial differential equations, III. Comput. Math. Appl. Part A 12 (1986), no. 4-5, 541--550.
 
12- Marcati, Pierangelo; Almost periodic solutions for a semilinear quasi-autonomous hyperbolic problem. Nonlinear Anal. 10 (1986), no. 10, 1053--1067.
 
11- Marcati, Pierangelo; Alcuni Risultati di Stabilitˆ  per Equazioni Astratte del Secondo Ordine in "Nonlinear Oscillations for Conservative Systems", Venezia 1985. (A.  Ambrosetti Ed.) Pitagora Editrice, Bologna.
 
10- Marcati, Pierangelo; Valli, Alberto Almost-periodic solutions to the Naviermhy Stokes equations for compressible fluids. Boll. Un. Mat. Ital. B (6) 4 (1985), no. 3, 969--986.
 
9- Marcati, P. On a nonconservative hyperbolic system describing the nonlinear age dependent populations growth. Hyperbolic partial differential equations, II. Comput. Math. Appl. 11 (1985), no. 1-3, 207--222.
 
8- Marcati, Pierangelo; Decay and stability for nonlinear hyperbolic equations. J. Differential Equations 55 (1984), no. 1, 30--58.
 
7- Marcati, Pierangelo; Stability for second order abstract evolution equations. Nonlinear Anal. 8 (1984), 237--252.
 
6- Marcati, Pierangelo; Asymptotic behavior of the renewal equation arising in the Gurtin population model. Nonlinear phenomena in mathematical sciences (Arlington, Tex., 1980), 655--662, Academic Press, New York-London, 1982.
 
5- Marcati, Pierangelo; Some considerations on the mathematical approach to nonlinear age dependent population dynamics. Hyperbolic partial differential equations. Comput. Math. Appl. 9 (1983), no. 3, 361--370.
 
4- Marcati, Pierangelo; On the global stability of the logistic age-dependent population growth. J. Math. Biol. 15 (1982), no. 2, 215--226.
 
3- Marcati, Pierangelo; Pozio, M. Assunta Global asymptotic stability for a vector disease model with spatial spread. J. Math. Biol. 9 (1980), no. 2, 179--187.
 
2- Marcati, Pierangelo; Serafini, Renato; Asymptotic behaviour in age dependent population dynamics with spatial spread. Boll. Un. Mat. Ital. B (5) 16 (1979), no. 2, 734--753.
 
1- Marcati, Pierangelo; Asymptotic behavior in age-dependent population dynamics with hereditary renewal law. SIAM J. Math. Anal. 12 (1981), no. 6, 904--916.

  
BOOKS  EDITED by P.MARCATI

1-  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)

2-  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.