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Mate.polimi.it

LIST OF PUBLICATIONS
[updated: May 2013]
[1] A. Remuzzi, B.M. Brenner, V. Pata, G. Tebaldo, R. Mariano, A. Belloro & G. Remuzzi, Three- dimensional reconstructed glomerular capillary network: blood flow distribution and local filtration, American Journal
of Physiology 263 (1992), F562–F572
[2] A. Remuzzi, P. Ruggenenti, L. Mosconi, V. Pata, G. Viberti & G. Remuzzi, Effect of low-dose Enalapril on glomerular size-selectivity in human diabetic nephropathy, Journal of Nephrology 6 (1993), 36–43
[3] H. Bercovici & V. Pata, Classical versus free domains of attractions, Mathematical Research Letters 2 (1995),
[4] V. Pata, L´evy type characterization of stable laws for free random variables, Transactions of the American Mathe- matical Society 347 (1995), 2457–2472
[5] H. Bercovici & V. Pata, The law of large numbers for free identically distributed random variables, The Annals of Probability 24 (1996), 453–465
[6] V. Pata, Domains of partial attraction in noncommutative probability, Pacific Journal of Mathematics 176 (1996),
[7] V. Pata, The central limit theorem for free additive convolution, Journal of Functional Analysis 140 (1996), 359–380
[8] V. Pata, A generalized weak law of large numbers for noncommuting random variables, Indiana University Mathe-
matics Journal 45 (1996), 591–601
[9] F. Gazzola & V. Pata, A uniform attractor for a non-autonomous generalized Navier-Stokes equation, Zeitschrift ur Analysis und ihre Anwendungen 16 (1997), 435–449
[10] J.M. Lindsay & V. Pata, Some weak laws of large numbers in non-commutative probability, Mathematische Zeitschrift 226 (1997), 533–543
[11] V. Pata, A note on strong convergence of noncommuting random variables, Bollettino della Unione Matematica Italiana B 11 (1997), 141–159
[12] V. Pata, A remark on the decay of strongly continuous semigroups of bounded linear operators, Rendiconti dell’Istituto Lombardo di Scienze e Lettere A 131 (1997), 143–149
[13] C. Giorgi, A. Marzocchi & V. Pata, Asymptotic behavior of a semilinear problem in heat conduction with memory, Nonlinear Differential Equations and Applications 5 (1998), 333–354
[14] M. Grasselli & V. Pata, Longtime behavior of a homogenized model in visco-elastodynamics, Discrete and Con- tinuous Dynamical Systems 4 (1998), 339–358
[15] V. Pata, Sulle soluzioni a crescenza lenta di equazioni differenziali ordinarie (in Italian), Rendiconti dell’Istituto Lombardo di Scienze e Lettere A 132 (1998), 71–83
[16] V. Pata, G. Prouse & M.I. Vishik, Traveling waves of dissipative nonautonomous hyperbolic equations in a strip, Advances in Differential Equations 3 (1998), 249–270
[17] H. Bercovici & V. Pata, Stable laws and domains of attraction in free probability theory, with an appendix by Ph.
Biane, Annals of Mathematics 149 (1999), 1023–1060
[18] S. Borini & V. Pata, Uniform attractors for a strongly damped wave equation with linear memory, Asymptotic Analysis 20 (1999), 263–277
[19] C. Giorgi, M. Grasselli & V. Pata, Uniform attractors for a phase-field model with memory and quadratic nonlinearity, Indiana University Mathematics Journal 48 (1999), 1395–1445
[20] V. Pata & P. Ursino, Rearrangeable functions on the real line, Real Analysis Exchange 24 (1998/99), 677–693
[21] H. Bercovici & V. Pata, A free analogue of Hinˇcin’s characterization of infinite divisibility, Proceedings of the American Mathematical Society 128 (2000), 1011–1015
[22] H. Bercovici & V. Pata, Functions of regular variation and freely stable laws, Annali di Matematica Pura ed Applicata 178 (2000), 245–269
[23] H. Bercovici & V. Pata, Limit laws for products of free and independent random variables, Studia Mathematica 141 (2000), 43–52
[24] A. Giarlotta, V. Pata & P. Ursino, Combinatorial and topological aspects of measure preserving homomorphisms, Topology Proceedings 25 (2000), 137–166
[25] C. Giorgi, A. Marzocchi & V. Pata, Uniform attractors for a non-autonomous semilinear heat equation with memory, Quarterly of Applied Mathematics 58 (2000), 661–683
[26] V. Pata, Attractors for a damped wave equation on IR3 with linear memory, Mathematical Methods in the Applied Sciences 23 (2000), 633–653
[27] V. Pata & E. Vuk, On the exponential stability of linear thermoelasticity, Continuum Mechanics and Thermody- namics 12 (2000), 121–130
[28] V. Pata, K.X. Zheng & A. Zucchi, On the reflexivity of operator algebras with isometric functional calculus, Journal of the London Mathematical Society 61 (2000), 604–616
[29] V. Pata & A. Zucchi, Reflexivity of C0-operators over a multiply connected region, Journal of Operator Theory 43
[30] V. Pata & A. Zucchi, Hyperinvariant subspaces of C0-operators over a multiply connected region, Integral Equations and Operator Theory 36 (2000), 241–250
[31] V. Belleri & V. Pata, Attractors for semilinear strongly damped wave equations on R3, Discrete and Continuous Dynamical Systems 7 (2001), 719–735
[32] C. Giorgi, M. Grasselli & V. Pata, Well-posedness and longtime behavior of the phase-field model with memory in a history space setting, Quarterly of Applied Mathematics 59 (2001), 701–736
noz Rivera & V. Pata, Global attractors for a semilinear hyperbolic equation in viscoelasticity, Journal of Mathematical Analysis and Applications 260 (2001), 83–99
[34] C. Giorgi, M.G. Naso & V. Pata, Exponential stability in linear heat conduction with memory: A semigroup approach, Communications in Applied Analysis 5 (2001), 121–134
[35] C. Giorgi & V. Pata, Stability of abstract linear thermoelastic systems with memory, Mathematical Models & Methods in Applied Sciences 11 (2001), 627–644
[36] C. Giorgi & V. Pata, Asymptotic behavior of a nonlinear hyperbolic heat equation with memory, Nonlinear Differ- ential Equations and Applications 8 (2001), 157–171
[37] M. Grasselli & V. Pata, Upper semicontinuous attractor for a hyperbolic phase-field model with memory, Indiana University Mathematics Journal 50 (2001), 1281–1308
[38] M. Grasselli & V. Pata, On the dissipativity of a hyperbolic phase-field system with memory, Nonlinear Analysis 47 (2001), 3157–3169
[39] V. Pata, Hyperbolic limit of parabolic semilinear heat equations with fading memory, Zeitschrift f¨ ihre Anwendungen 20 (2001), 359–377
[40] V. Pata & C. Santina, Longtime behavior of semilinear reaction-diffusion equations on the whole space, Rendiconti del Seminario Matematico dell’Universit` a di Padova 105 (2001), 233–251
[41] V. Pata & A. Zucchi, Attractors for a damped hyperbolic equation with linear memory, Advances in Mathematical Sciences and Applications 11 (2001), 505–529
[42] M. Grasselli & V. Pata, On the longterm behaviour of a parabolic phase-field model with memory, in “Differential equations and control theory” (S. Aizicovici and N.H. Pavel, Eds.), pp.147–157, Lecture Notes in Pure and Appl.
Math. no.225, Marcel Dekker, New York (2002) [43] M. Grasselli & V. Pata, Uniform attractors of nonautonomous systems with memory, in “Evolution equations, semigroups and functional analysis” (A. Lorenzi and B. Ruf, Eds.), pp.155–178, Progr. Nonlinear Differential Equa-tions Appl. no.50, Birkh¨ [44] M. Grasselli & V. Pata, Phase-field system with memory effects in the order parameter dynamics, in “Mathe- matical models and methods for smart materials” (M. Fabrizio, B. Lazzari and A. Morro, Eds.), pp.155–164, Ser. onAdv. Math. Sci. Appl. no.62, World Scientific, Singapore (2002) [45] V. Pata & A. Villani, Some measurability and continuity properties of arbitrary real functions, Le Matematiche 57 (2002), 63–82
[46] M. Grasselli & V. Pata, On the damped semilinear wave equation with critical exponent, Dynamical systems and differential equations (Wilmington, NC, 2002). Discrete and Continuous Dynamical Systems (suppl.) (2003), 351–358 [47] M. Grasselli & V. Pata, Existence of a universal attractor for a parabolic-hyperbolic phase-field system, Advances in Mathematical Sciences and Applications 13 (2003), 443–459
[48] M. Grasselli, V. Pata & F.M. Vegni, Longterm dynamics of a conserved phase-field system with memory, Asymptotic Analysis 33 (2003), 261–320
[49] S. Gatti, M. Grasselli & V. Pata, Exponential attractors for a phase-field model with memory and quadratic nonlinearity, Indiana University Mathematics Journal 53 (2004), 719–754
[50] S. Gatti, M. Grasselli & V. Pata, Exponential attractors for a conserved phase-field system with memory, Physica D 189 (2004), 31–48
[51] M. Grasselli & V. Pata, Existence of a universal attractor for a fully hyperbolic phase-field system, Journal of Evolution Equations 4 (2004), 27–51
[52] M. Grasselli & V. Pata, Attractor for a conserved phase-field system with hyperbolic heat conduction, Mathematical Methods in the Applied Sciences 27 (2004), 1917–1934
[53] M. Grasselli & V. Pata, Asymptotic behavior of a parabolic-hyperbolic system, Communications on Pure and Applied Analysis 3 (2004), 849–881
[54] M. Grasselli, V. Pata & G. Prouse, Longtime behavior of a viscoelastic Timoshenko beam, Discrete and Con- tinuous Dynamical Systems 10 (2004), 337–348
[55] M. Conti & V. Pata, Weakly dissipative semilinear equations of viscoelasticity, Communications on Pure and Applied Analysis 4 (2005), 705–720
[56] M. Conti, V. Pata & M. Squassina, Strongly damped wave equations on R3 with critical nonlinearities, Commu- nications in Applied Analysis 9 (2005), 161–176
[57] M. Conti, V. Pata & M. Squassina, Singular limit of dissipative hyperbolic equations with memory, Discrete and Continuous Dynamical Systems (suppl.) (2005), 200–208 [58] S. Gatti, C. Giorgi & V. Pata, Navier-Stokes limit of Jeffreys type flows, Physica D 203 (2005), 55–79
[59] S. Gatti, M. Grasselli, A. Miranville & V. Pata, Hyperbolic relaxation of the viscous Cahn-Hilliard equation
in 3-D, Mathematical Models & Methods in Applied Sciences 15 (2005), 165–198
[60] S. Gatti, M. Grasselli, A. Miranville & V. Pata, On the hyperbolic relaxation of the one-dimensional Cahn- Hilliard equation, Journal of Mathematical Analysis and Applications 312 (2005), 230–247
[61] S. Gatti, M. Grasselli, A. Miranville & V. Pata, Memory relaxation of first order evolution equations, Nonlinearity 18 (2005), 1859–1883
[62] S. Gatti, M. Grasselli & V. Pata, Lyapunov functionals for reaction-diffusion equations with memory, Mathe- matical Methods in the Applied Sciences 28 (2005), 1725–1735
[63] S. Gatti, M. Grasselli, V. Pata & M. Squassina, Robust exponential attractors for a family of nonconserved phase-field systems with memory, Discrete and Continuous Dynamical Systems 12 (2005), 1019–1029
[64] C. Giorgi, M.G. Naso & V. Pata, Energy decay of electromagnetic systems with memory, Mathematical Models & Methods in Applied Sciences 15 (2005), 1489–1502
noz Rivera & V. Pata, On the energy decay of the linear thermoelastic plate with memory, Journal of Mathematical Analysis and Applications 309 (2005), 1–14
[66] M. Grasselli & V. Pata, Robust exponential attractors for a phase-field system with memory, Journal of Evolution Equations 4 (2005), 465–483
[67] M. Grasselli & V. Pata, Attractors of phase-field systems with memory, in “Mathematical methods and models in phase transitions” (A. Miranville, Ed.), pp.157–175, Nova Science Publishers, Inc., New York (2005) [68] A. Miranville & V. Pata, On the semilinear wave equation with locally distributed nonlinear damping, in “Math- ematical approach to nonlinear phenomena; modelling, analysis and simulations”, pp.188–197, GAKUTO Internat.
Ser. Math. Sci. Appl. no.7, Gakk¯ [69] V. Pata & M. Squassina, On the strongly damped wave equation, Communications in Mathematical Physics 253
[70] V.V. Chepyzhov, S. Gatti, M. Grasselli, A. Miranville & V. Pata, Trajectory and global attractors for evolution equations with memory, Applied Mathematics Letters 19 (2006), 87–96
[71] V.V. Chepyzhov, E. Mainini & V. Pata, Stability of abstract linear semigroups arising from heat conduction with memory, Asymptotic Analysis 50 (2006), 269–291
[72] V.V. Chepyzhov & V. Pata, Some remarks on stability of semigroups arising from linear viscoelasticity, Asymptotic Analysis 46 (2006), 251–273
[73] M. Conti, V. Pata & M. Squassina, Singular limit of differential systems with memory, Indiana University Mathematics Journal 55 (2006), 169–216
[74] S. Gatti, M. Grasselli, A. Miranville & V. Pata, A construction of a robust family of exponential attractors, Proceedings of the American Mathematical Society 134 (2006), 117–127
[75] S. Gatti, M. Grasselli, A. Miranville & V. Pata, Memory relaxation of the one-dimensional Cahn-Hilliard equation, in “Dissipative phase transitions” (P. Colli, N. Kenmochi and J. Sprekels, Eds.), pp.101–114, Ser. Adv.
Math. Appl. Sci. 71, World Sci. Publ., Hackensack, NJ (2006) [76] S. Gatti & V. Pata, A one-dimensional wave equation with nonlinear damping, Glasgow Mathematical Journal 48
[77] M. Grasselli & V. Pata, A reaction-diffusion equation with memory, Discrete and Continuous Dynamical Systems 15 (2006), 1079–1088
[78] V. Pata, Exponential stability in linear viscoelasticity, Quarterly of Applied Mathematics 64 (2006), 499–513
[79] V. Pata & S. Zelik, A remark on the damped wave equation, Communications on Pure and Applied Analysis 5
[80] V. Pata & S. Zelik, Global and exponential attractors for 3-D wave equations with displacement dependent damping, Mathematical Methods in the Applied Sciences 29 (2006), 1291–1306
[81] V. Pata & S. Zelik, Smooth attractors for strongly damped wave equations, Nonlinearity 19 (2006), 1495–1506
[82] S. D’Asero, V. Pata & P. Ursino, On a generalized notion of differentiability, Real Analysis Exchange 32
[83] M. Conti, S. Gatti & V. Pata, Decay rates of Volterra equations on RN , Central European Journal of Mathematics 5 (2007), 720–732
[84] M. Grasselli, A. Miranville, V. Pata & S. Zelik, Well-posedness and long time behavior of a parabolic- hyperbolic phase-field system with singular potentials, Mathematische Nachrichten 280 (2007), 1475–1509
[85] A. Miranville, V. Pata & S. Zelik, Exponential attractors for singularly perturbed damped wave equations: a simple construction, Asymptotic Analysis 53 (2007), 1–12
[86] V. Pata & S. Zelik, A result on the existence of global attractors for semigroups of closed operators, Communications on Pure and Applied Analysis 6 (2007), 481–486
[87] V. Pata & S. Zelik, Attractors and their regularity for 2-D wave equations with nonlinear damping, Advances in Mathematical Sciences and Applications 17 (2007), 225–237
[88] V.V. Chepyzhov, V. Pata, & M.I. Vishik, Averaging of nonautonomous damped wave equations with singularly oscillating external forces, Journal de Math´ ees 90 (2008), 469–491
[89] M. Conti, S. Gatti & V. Pata, Uniform decay properties of linear Volterra integro-differential equations, Mathe- matical Models & Methods in Applied Sciences 18 (2008), 21–45
[90] F. Di Plinio & V. Pata, Robust exponential attractors for the strongly damped wave equation with memory. I, Russian Journal of Mathematical Physics 15 (2008), 301–315
[91] F. Di Plinio, V. Pata & S. Zelik, On the strongly damped wave equation with memory, Indiana University Mathematics Journal 57 (2008), 757–780
[92] S. Gatti, A. Miranville, V. Pata & S. Zelik, Attractors for semilinear equations of viscoelasticity with very low dissipation, Rocky Mountain Journal of Mathematics 38 (2008), 1117–1138
[93] C. Giorgi, V. Pata & E. Vuk, On the extensible viscoelastic beam, Nonlinearity 21 (2008), 713–733
[94] M.I. Vishik, V. Pata & V.V. Chepyzhov, Time averaging of global attractors for nonautonomous wave equations
with singularly oscillating external forces (in Russian), Doklady Akademii Nauk 422 (2008), 164–168
[95] V.V. Chepyzhov, V. Pata & M.I. Vishik, Averaging of 2D Navier-Stokes equations with singularly oscillating forces, Nonlinearity 22 (2009), 351–370
[96] M. Conti & V. Pata, On the regularity of global attractors, Discrete and Continuous Dynamical Systems 25 (2009),
[97] F. Di Plinio & V. Pata, Robust exponential attractors for the strongly damped wave equation with memory. II, Russian Journal of Mathematical Physics 16 (2009), 61–73
[98] S. Gatti, V. Pata & S. Zelik, A Gronwall-type lemma with parameter and dissipative estimates for PDEs, Non- linear Analysis 70 (2009), 2337–2343
[99] C. Giorgi, M.G. Naso, V. Pata & M. Potomkin Global attractors for the extensible thermoelastic beam system, Journal of Differential Equations 246 (2009), 3496–3517
[100] V. Pata, Gradient systems of closed operators, Central European Journal of Mathematics 7 (2009), 487–492
[101] V. Pata, Stability and exponential stability in linear viscoelasticity, Milan Journal of Mathematics 77 (2009), 333–360
[102] M. Conti, S. Gatti, M. Grasselli & V. Pata, Two-dimensional reaction-diffusion equations with memory, Quarterly of Applied Mathematics 68 (2010), 607-643
[103] M. Conti, E.M. Marchini & V. Pata, Semilinear wave equations of viscoelasticity in the minimal state framework, Discrete and Continuous Dynamical Systems 27 (2010), 1535–1552
[104] M. Coti Zelati, C. Giorgi & V. Pata, Steady states of the hinged extensible beam with external load, Mathematical Models & Methods in Applied Sciences 20 (2010), 43–58
[105] M. Coti Zelati, V. Pata & R. Quintanilla, Regular global attractors of type III thermoelastic extensible beams, Chinese Annals of Mathematics - Series B 31 (2010), 619–630
[106] M. Fabrizio, C. Giorgi & V. Pata, A new approach to equations with memory, Archive for Rational Mechanics and Analysis 198 (2010), 189–232
[107] S. Gatti, A. Miranville, V. Pata & S. Zelik, Continuous families of exponential attractors for singularly perturbed equations with memory, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140A
(2010), 329–366
[108] V. Pata, Exponential stability in linear viscoelasticity with almost flat memory kernels, Communications on Pure and Applied Analysis 9 (2010), 721–730
[109] V. Pata & R. Quintanilla, On the decay of solutions in nonsimple elastic solids with memory, Journal of Mathe- matical Analysis and Applications 363 (2010), 19–28
[110] M.D. Chekroun, F. Di Plinio, N.E. Glatt-Holtz & V. Pata, Asymptotics of the Coleman-Gurtin model, Discrete and Continuous Dynamical Systems - Series S 4 (2011), 351–369
[111] F. Dell’Oro & V. Pata, Long-term analysis of strongly damped nonlinear wave equations, Nonlinearity 24 (2011),
[112] E. Laeng & V. Pata, A convergence-divergence test for series of nonnegative terms, Expositiones Mathematicae 29 (2011), 420–424
[113] V. Pata, Uniform estimates of Gronwall type, Journal of Mathematical Analysis and Applications 373 (2011),
[114] V. Pata, A fixed point theorem in metric spaces, Journal of Fixed Point Theory and Applications 10 (2011), 299–305
[115] V.V. Chepyzhov, M. Conti & V. Pata, A minimal approach to the theory of global attractors, Discrete and Continuous Dynamical Systems 32 (2012), 2079–2088
[116] M. Conti, E.M. Marchini & V. Pata, Approximating infinite delay with finite delay, Communications in Con- temporary Mathematics 14 (2012), no.1250012
[117] F. Dell’Oro & V. Pata, Strongly damped wave equations with critical nonlinearities, Nonlinear Analysis 75 (2012),
[118] F. Dell’Oro & V. Pata, Memory relaxation of type III thermoelastic extensible beams and Berger plates, Evolution Equations and Control Theory 1 (2012), 251–270
[119] V. Pata, On the regularity of solutions to the Navier-Stokes equations, Communications on Pure and Applied Analysis 11 (2012), 747–761
[120] M. Conti, E.M. Marchini & V. Pata, Exponential stability for a class of linear hyperbolic equations with hereditary memory, Discrete and Continuous Dynamical Systems - Series B 18 (2013), 1555–1565
[121] M. Coti Zelati, F. Dell’Oro & V. Pata, Energy decay of type III linear thermoelastic plates with memory, Journal of Mathematical Analysis and Applications 401 (2013), 357–366
[122] V.V. Chepyzhov, M. Conti & V. Pata, Totally dissipative dynamical processes and their uniform global attractors, Communications on Pure and Applied Analysis [123] M. Conti, E.M. Marchini & V. Pata, Reaction-diffusion with memory in the minimal state framework, Transac- tions of the American Mathematical Society [124] M. Conti, V. Pata & R. Temam, Attractors for processes on time-dependent spaces. Applications to wave equations, [125] C. Giorgi, D. Grandi & V. Pata, On the Green-Naghdi type III heat conduction model, Discrete and Continuous Preprints
[126] M. Conti, F. Dell’Oro & V. Pata, Timoshenko systems with fading memory[127] M. Conti, E.M. Marchini & V. Pata, Nonclassical diffusion with memory[128] M. Conti & V. Pata, Asymptotic structure of the attractor for processes on time-dependent spaces[129] F. Dell’Oro, J.E. Mu˜ noz Rivera & V. Pata, Exponential and polynomial stability of linear thermoelastic plates [130] F. Dell’Oro & V. Pata, On the stability of Timoshenko systems with Gurtin-Pipkin thermal law

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