Elisabetta Rocca - List of publications


WARNING:
The electronic files included here
are the preprint versions and
NOT the final published ones.

updated to August 26, 2019

Pubblished papers on International Journals and on Scientific Volumes

90. A. Miranville, E. Rocca, G. Schimperna,
On the long time behavior of a tumor growth model,
Journal of Differential Equations, 67 (2019),  261--2642.

89. P. Colli, G. Gilardi, G. Marinoschi, E. Rocca,
Sliding mode control for phase field system related to tumor growth,
Applied Mathematics & Optimization,
79 (2019), 647--670.

88. C. Cavaterra, E. Rocca, H. Wu,
Long-time Dynamics and Optimal Control of a Diffuse Interface Model for Tumor Growth,
Applied Mathematics & Optimization,
DOI: 10.1007/s00245-019-09562-5 (2019).

87. A. Miranville, E. Rocca, G. Schimperna,
On the long time behavior of a tumor growth model,
Journal of Differential Equations,
67 (2019),  261--2642.

86. P. Colli, G. Gilardi, G. Marinoschi, E. Rocca,
Sliding mode control for phase field system related to tumor growth,
Appl. Math. Optim., 79 (2019), 647--670.

85. H. Garcke, K.-F. Lam, E. Rocca,
Optimal control of treatment time in a diffuse interface model of tumor growth,
Appl. Math. Optim., 78 (2018), 495--544.

84. P. Colli, G. Gilardi, G. Marinoschi, E. Rocca,
Distributed optimal control problems for phase field systems with singular potential,
Analele Stiintifice ale Universitatii Ovidius Constanta. Seria Matematica, 26 (2018), 71--85.

83. S. Frigeri, K.-F. Lam, E. Rocca, G. Schimperna,
On a multi-species Cahn-Hilliard-Darcy tumor growth model with singular potentials,
Comm Math Sci., 16 (2018), 821--856.

82. E. Feireisl, E. Rocca, G. Schimperna, A. Zarnescu,
On a hyperbolic system arising in liquid crystals modeling,
Journal of Hyperbolic Differential Equations, 15 (2018), 15--35.

81. B. Detmann, P. Krejci Pavel, E. Rocca
Periodic waves in unsaturated porous media with hysteresis,
in Proceedings of the European Congress of Mathematics, Berlin, 18.7.2016 - 22.7.2016, e
ditor(s): Volker Mehrmann, Martin Skutella, European Congress of Mathematics,
European Mathematical Society Publishing House, Zurich, 2018, 219-234.

80. M. Fre'mond, M. Marino, E. Rocca,
Collisions in shape memory alloys,
GAMM-Mitt. 40, No. 3, 157-177 (2017) / DOI 10.1002/gamm.201730002 .

79. P. Colli, G. Gilardi, G. Marinoschi, E. Rocca,
Optimal control for a conserved phase field system with a possibly singular potential,
EVOLUTION EQUATIONS AND CONTROL THEORY, 7  (2018), 95--116.

78. S. Melchionna, E. Rocca,
Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth,
 Interfaces and Free Boundaries, 19 (2018), 571--590.

77. P. Krejci, E. Rocca, J. Sprekels,
Unsaturated deformable porous media flow with phase transition,
Math. Models Methods Appl. Sci., 27 (2017), 2675--2710.

76. S. Frigeri, K.-F. Lam, E. Rocca,
On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities,
 In: P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels (eds.), Solvability,
Regularity, Optimal Control of Boundary Value Problems for PDEs,
pp.~217--254, Springer INdAM Series, Springer, Milan, 2017.

75. E. Bonetti, E. Rocca, R. Scala, G. Schimperna,
On the strongly damped wave equation with constraint,
Commun. Part. Diff. Eq., 42 (2017), 1042--1064.

74. V. Barbu, P. Colli, G. Gilardi, G. Marinoschi, E. Rocca,
Sliding mode control for a nonlinear phase-field system,
SIAM J. Control Optim. 55 (2017), 2108--2133.

73. P. Colli, G. Gilardi, E. Rocca, J. Sprekels,
Optimal distributed control of a diffuse interface model of tumor growth,  
Nonlinearity 30 (2017), 2518--2546.

72. E. Bonetti, E. Rocca,
Unified gradient flow structure of phase field systems via a generalized principle of virtual powers,
ESAIM : COCV,  23 (2017), 1201--1216.

71. E. Rocca, R. Scala,
A rigorous sharp interface limit of a diffuse interface model related to tumor growth,
J. Nonlinear Sci., 27 (2017), 847--872.

70. C. Heinemann, C. Kraus, E. Rocca, R. Rossi, 
A temperature-dependent phase-field model for phase separation and damage,
Arch. Ration. Mech. Anal., 225 (2017), 177--247.

69. M. Dai, E. Feireisl, E. Rocca, G. Schimperna, M. Schonbek,
Analysis of a diffuse interface model of multispecies tumor growth,
Nonlinearity, 30 (2017), 1639.

68. C. Cavaterra, E. Rocca, H. Wu,
Optimal boundary control of a simplified Ericksen–Leslie system for nematic liquid crystal flows in 2D,
Arch. Ration. Mech. Anal., 224 (2017), 1037--1086.

67. P. Colli, G. Gilardi, E. Rocca, J. Sprekels,
Asymptotic analyses and error estimates for a Cahn–Hilliard type phase field system modelling tumor growth,
Discrete Contin. Dyn. Syst. Ser. S, 10 (2017), 37--54.

66. B. Detmann, P. Krejci, E. Rocca,
Solvability of an unsaturated porous media flow problem with thermomechanical interaction,
SIAM J. Math. Anal., 48 (2016), 4175--4201.

65. M. Eleuteri, E. Rocca, G. Schimperna,
Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids,
Ann. Inst. H. Poincare Anal. Non Lineaire, 33 (2016), 1431-1454.

64. M. Dai, E. Feireisl, E. Rocca, G. Schimperna, M. Schonbek,
On asymptotic isotropy for a hydrodynamic model of liquid crystals,
Asymptot. Anal, 97 (2016), 189-210.

63. E. Bonetti, E. Rocca, R. Rossi, M. Thomas,
A rate-independent gradient system in damage coupled with plasticity via structured strains,
ESAIM: PROCEEDINGS AND SURVEYS, 54 (2016), 54-69.

62. C. Cavaterra, E. Rocca, H. Wu, X. Xu,
Global strong solutions of the full Navier-Stokes and Q-tensor system for nematic liquid crystal flows in 2D: existence and long-time behavior,
SIAM J. Math. Anal. 48 (2016), no. 2, 1368-1399.

61. P. Colli, G. Marinoschi, E. Rocca,
Sharp interface control in a Penrose-Fife model,
ESAIM: COCV 22 (2016), 473-499.

60. S. Frigeri, E. Rocca, J. Sprekels,
Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes system in 2D,
SIAM J. Control Optim. 54 (2016), 221-250.

59. P. Colli, G. Gilardi, G. Marinoschi, E. Rocca,
Optimal control  for a phase field system with a possibly singular potential,
Math. Control Relat. Fields, 6 (2016), 95-112.

58. C. Heinemann, E. Rocca,
Damage processes in thermoviscoelastic materials with damage-dependent thermal expansion coefficients,
MMAS,  38 (2015), 4587--4612.

57. E. Feireisl, E. Rocca, G. Schimperna, A. Zarnescu,
Nonisothermal nematic liquid crystal flows with the Ball-Majumdar free energy,
Annali di Matematica, 194 (2015), 1269--1299.

56. E. Rocca, J. Sprekels,
Optimal distributed control of a nonlocal convective Cahn-Hilliard equation by the velocity in 3D,
SIAM J. Control Optim., 53 (2015), 1654--1680.

55. E. Rocca, R. Rossi,
``Entropic'' solutions to a thermodynamically consistent PDE system for phase transitions and damage,
SIAM J. Math. Anal., 47 (2015), 2519--2586.

54. P. Colli, G. Gilardi, E. Rocca, J. Sprekels,
Vanishing viscosities and error estimate for a Cahn--Hilliard type phase-field system related to tumor growth,
Nonlinear Analysis: Real World Applications, 26 (2015), 93--108.

53. S. Frigeri, M. Grasselli, E. Rocca, 
A diffuse interface model for two-phase incompressible flows with nonlocal interactions and nonconstant mobility,
Nonlinearity,  28 (2015), 1257--1293.

52. S. Frigeri, M. Grasselli, E. Rocca,
 On a diffuse interface model of tumor growth,
European J. Appl. Math., 26 (2015), 215--243.

51. M. Eleuteri, E. Rocca, G. Schimperna,
On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids,
Discrete Contin. Dyn. Syst., 35 (2015), 2497--2522.

50. D. Hoemberg, T. Petzold, E. Rocca,
Analysis and simulation of multifrequency induction hardening,
Nonlinear Analysis: Real World Applications, 22 (2015), 84–-97.

49. S. Melchionna, E. Rocca,
On a nonlocal Cahn-Hilliard equation with a reaction term,
Adv. Math. Sci. Appl., 24 (2014), 461--497.

48. D. Hoemberg, T. Petzold, E. Rocca,
Multifrequency induction hardening: a challenge for industrial mathematics,
in ``The Impact of Applications on Mathematics'', Mathematics for Industry 1, M. Wakayama et al. (eds.), Springer, Japan (2014).

47. A. Miranville, E. Rocca, G. Schimperna, A. Segatti,
The Penrose-Fife phase-field model with coupled dynamic boundary conditions
Discrete Contin. Dyn. Syst. , 34 (2014), 4259--4290.

46. E. Rocca, R. Rossi,
A degenerating PDE system for phase transitions and damage,
Math. Models Methods Appl. Sci., 24 (2014), 1265--1341.

45. E. Feireisl, E. Rocca, G. Schimperna, A. Zarnescu,
Evolution of non-isothermal Landau-de Gennes nematic liquid crystals flows with singular potential,
Comm. Math. Sci., 12 (2014), 317--343.

44. C. Cavaterra, E. Rocca, H. Wu,
Global weak solution and blow-up criterion of the general Ericksen--Leslie system for nematic liquid crystal flows,
J. Differential Equations, 255 (2013), 24--57.


43. S. Frigeri, E. Rocca,
Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D,
Nonlinearity, 26 (2013), 933--957.

42.  C. Cavaterra, E. Rocca,
On a 3D isothermal model for nematic liquid crystals accounting for stretching terms,
Z. Angew. Math. Phys., 64 (2013), 69--82.

41. P. Krejci, E. Rocca,
Well-posedness of an extended model for water-ice phase transitions,
Discrete Contin. Dyn. Syst. Ser. S, 6, no.2 (2013), 439--460.

40. H.  Petzeltova, E. Rocca, G. Schimperna,
On the long-time behavior of some mathematical models for nematic liquid crystals,
Calc. Var., 46 (2013), 623-639.

39. E. Feireisl, M. Fre'mond, E. Rocca, G. Schimperna,
A new approach to non-isothermal models for nematic liquid crystals,
Arch. Ration. Mech. Anal. 205 (2012), no. 2, 651-672.

38.  D. Hoemberg, E. Rocca,
A model for resistance welding including phase transitions and Joule heating,
Math. Meth. Appl. Sci. 2011, 34,  2077--2088.

37. P. Colli, P. Krejci, E. Rocca, J. Sprekels,
A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity,
J. Differential Equations,  251 (2011), 1354--1387.

36. E. Feireisl, E. Rocca, G. Schimperna,
 On a non-isothermal model for nematic liquid crystals,
Nonlinearity, 24 (2011), 243--257.

35. P. Krejci, E. Rocca , J. Sprekels,
Phase separation in a gravity field,
Discrete Contin. Dyn. Syst. Ser. S, 4, No. 2 (2011), 391--407.

34. M. Fremond, E. Rocca,
A model for shape memory alloys with the possibility of voids,
Discrete Contin. Dyn. Syst., 27 No. 4 (2010), 1633--1659.

33. E. Feireisl, H. Petzeltova, E. Rocca, G. Schimperna,
Analysis of a phase-field model for two-phase compressible fluids,
Math. Models Methods Appl. Sci., 20 No. 7 (2010).

32. P. Krejci, E. Rocca, J. Sprekels,
Liquid-solid phase transitions in a deformable container,
contribution to the book ``Continuous Media with Microstructure'' on the occasion of Krzysztof Wilmanski's 70th birthday, Springer (2010), 285--300.

31.  P. Krejci, E. Rocca, J. Sprekels,
A bottle in a freezer
SIAM J. Math. Anal., 41 No. 5 (2009),  1851--1873.

30. E. Feireisl, H. Petzeltova, E. Rocca,
Existence of solutions to some models of phase changes with microscopic movements,
Math. Meth. Appl. Sci., 32 (2009), 1345--1369.

29. M. Fremond, E. Rocca,
Solid liquid phase changes with different densities,
Quart. Appl. Math., 66 (2008), 609--632.

28. E. Rocca, R. Rossi,
Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials,
Appl. Math., 53 No. 5 (2008), 485--520.

27. E. Rocca, R. Rossi,
Analysis of a nonlinear degenerating PDE system for phase transitions in thermoviscoelastic materials,
J. Differential Equations, 245 (2008), 3327--3375.

26. A. Lorenzi, E. Rocca,
Identification of two memory kernels in a fully hyperbolic phase-field system,
J. Inverse Ill-Posed Probl., 16 (2008), 147--174.

25. P. Colli, P. Krejci, E. Rocca, J. Sprekels,
Nonlinear evolution inclusions arising from phase change models,
Czech. Math. J., 57 (2007), 1067--1098.

24. E. Bonetti, M. Fremond, E. Rocca,
A new dual approach for a class of phase transitions with memory: existence and long-time behaviour of solutions,
J. Math. Pures Appl., 88 (2007), 455--481.

23. G. Gilardi, E. Rocca,
Well posedness and long time behaviour for a singular phase field system of conserved type,
IMA J. Appl. Math., 72 (2007), 498--530.

22. P. Krejci, E. Rocca, J. Sprekels,
A nonlocal phase-field model  with nonconstant specific heat,
Interfaces Free Bound., 9 (2007), 285--306.

21.  A. Lorenzi, E. Rocca,
Weak solutions for the fully hyperbolic phase-field system of conserved type,
J. Evol. Equ., 7 (2007), 59--78.

20. E. Bonetti, E. Rocca,
Global  existence and long-time behaviour for a singular integro-differential phase-field system,
Commun. Pure Appl. Anal, 6 (2007), 367--387.

19. P. Krejci, E. Rocca, J. Sprekels,
Nonlocal temperature-dependent phase-field models for non-isothermal phase transitions,
J. London Math. Soc., 76  No. 2 (2007), 197--210.

18. G. Gilardi, E. Rocca,
Convergence of phase field to phase relaxation governed by the entropy balance with memory,
Math. Meth. Appl. Sci., 29 (2006), 2149--2179.

17. A. Lorenzi, E. Rocca,
Approximation of an inverse problem for a parabolic integro-differential system of Caginalp type,
in ``Dissipative phase transitions'' (ed. P. Colli, N. Kenmochi, J. Sprekels), Series on Advances in Mathematics for Applied Sciences, Vol. 71,  World Sci. Publishing (2006), 151--176.

16. P. Colli, M. Fremond, E. Rocca, K. Shirakawa,
Attractors for the 3D Fremond model of shape memory alloys,
Chinese Annals of Mathematics, Ser. B, 27 (2006), 683--700.

15. E. Rocca, G. Schimperna,
Global attractor for a parabolic-hyperbolic Penrose-Fife phase field system,
Discrete Contin. Dyn. Syst., 15 No. 4 (2006), 1192--1214.

14. M. Fremond, E. Rocca,
Well-posedness of a phase transition model with the possibility of voids,
Math. Models Methods Appl. Sci., 16 No. 4 (2006), 559--586.

13. A. Lorenzi, E. Rocca, G. Schimperna,
Direct and inverse problems for parabolic integro-differential systems of Caginalp type,
Adv. Math. Sci. Appl., 15 No. 1 (2005), 227--263.

12. E. Rocca,
Well-posedness and regularity for a parabolic-hyperbolic Penrose-Fife phase field system,
Appl. Math.,  50 No. 5 (2005), 415--450.

11. E. Rocca, G. Schimperna,
Universal attractor for a Penrose-Fife system with special heat flux law,
Mediterr. J. Math., 1 (2004), 109--121.

10. E. Rocca, G. Schimperna,
Universal attractor for some singular phase transition systems,
Physica D, 192 (2004), 279--307.

9. P. Colli, G. Gilardi, E. Rocca, G. Schimperna,
On a Penrose-Fife phase-field model with non-homogeneous Neumann boundary condition for the temperature,
Differential and Integral Equations, 17  No. 5--6 (2004), 511--534.

8. E. Rocca,
Existence and uniqueness for the parabolic conserved phase field model with memory,
Commun. Appl. Anal., 8 No. 1 (2004), 27--46.

7. E. Rocca,
The conserved Penrose-Fife system with temperature-dependent memory,
J. Math. Anal. Appl., 287 No. 1 (2003), 177--199.

6. E. Rocca, G. Schimperna,
Singular limits of a conserved Penrose-Fife phase field model with special heat flux laws and memory effects,
Asymptot. Anal., 36 No. 3--4 (2003), 285--301.

5. E. Rocca, G. Schimperna,
The Conserved Penrose-Fife system with Fourier heat flux law
Nonlinear Anal., 53 (2003), 1089--1100.

4. G. Gilardi, E. Rocca,
Su un modello conservativo di tipo Penrose-Fife con condizioni di Neumann,
Istituto Lombardo (Rend. Sc.) A, 136-137 (2002--2003).

3. E. Rocca,
Some remarks on the conserved Penrose-Fife phase field model with memory effects,
in ``Mathematical Models and Methods for Smart Materials'', M. Fabrizio, B. Lazzari, and  A. Morro (ed.), Ser.Adv.Math.Appl.Sci., 62, World Scientific Publishing Co. (2002), 313--322.

2. E. Rocca,
The conserved Penrose-Fife phase field model with special heat flux laws and memory effects,
J. Integral Equations Appl., 14 No. 4 (2002), 425--466.

1. E. Rocca,
Asymptotic analysis of a conserved phase-field model with memory for vanishing time relaxation, 
Adv. Math. Sci. Appl., 10 No. 2 (2000), 899--916.

Preprints and papers to appear:

1. M. Carraturo, E. Rocca, E. Bonetti, D. Hoemberg,  A. Reali, A. Auricchio,
Additive Manufacturing Graded-material Design based on
Phase-field and Topology Optimization,
arXiv:1811.07205v2 (2018), to appear on Computational Mechanics (2019).

2. M. Carraturo, E. Rocca, E. Bonetti, D. Hoemberg,  A. Reali, A. Auricchio, 
Structural multiscale topology optimization with stress constraint for additive
manufacturing, arXiv:1907.06355v1 (2019).

3. R. Lasarzik, E. Rocca, G. Schimperna,
Weak solutions and weak-strong uniqueness for a
thermodynamically consistent phase-field model,  arXiv:1907.12816 (2019).

4. P. Colli, H. Gomez, G. Lorenzo, G. Marinoschi, A. Reali, E. Rocca,
Mathematical analysis and simulation study of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects,     arXiv:1907.11618 (2019).

5. C. Orrieri, L. Scarpa, E. Rocca,
Optimal control of stochastic phase-field models related to tumor growth, arXiv:1908.00306v1 (2019).


Editor of the volumes:

[V2] ``Special issue dedicated to Michel Fre'mond on the occasion of his 70th birthday'',
Discrete Contin. Dyn. Syst. Ser. S, 6, No. 2 (2013), edited by E. Bonetti, C. Cavaterra, E. Rocca, R. Rossi.

[V1] ``New trends in direct, inverse, and control problems for evolution equations'',
Discrete Contin. Dyn. Syst. Ser. S, 4, No. 3 (2011), edited by P. Cannarsa, C. Cavaterra,  A. Favini, A. Lorenzi, E. Rocca.

[V3] ``Special issue on rate-independent evolutions and hysteresis modelling'',
Discrete Contin. Dyn. Syst. Ser. S, 8, No. 4 (2015), edited by S. Bosia, M. Eleuteri, E. Rocca, and E. Valdinoci.

[V4] ``Special issue dedicated to Juergen Sprekels on the occasion of his 65th birthday'',
Discrete Contin. Dyn. Syst., 35, No. 6 (2015), edited by P. Colli,  G. Gilardi,  D. Hoemberg,  P. Krejci and Elisabetta Rocca.

[V5] ``PDE 2015: Theory and applications of partial differential equations'', edited by Hans-Christoph Kaiser,  Dorothee Knees,  Alexander Mielke,  Joachim Rehberg,  Elisabetta Rocca,  Marita Thomas and Enrico Valdinoci,  Discrete Contin. Dyn. Syst. Ser. S, 10, No. 4 (2017).

[V6] ``Solvability, Regularity, Optimal Control of Boundary Value Problems for PDEs'',
edited by P.~Colli, A.~Favini, E.~Rocca, G.~Schimperna, J.~Sprekels,
Springer INdAM Series, Springer, Milan, 2017.

[V7] ``Trends on Applications of Mathematics to Mechanics'', edited by
E. Rocca, U. Stefanelli, L. Truskinovsky, and A. Visintin, Springer INdAM Series, Springer, Milan, 2017.

[V8] ``Mathematical Thermodynamics of Complex Fluids'', edited by E. Feireisl and E. Rocca, 
Springer CIME Series, Springer, Milan, 2017.

[V9] M. Hintermueller, K. Kunisch, G. Leugering, E. Rocca, ``Challenges in Optimal Control of Nonlinear PDE-Systems'',
Oberwolfach Rep. 15 (2018), no. 2, 941--1020.

Other publications:

[N.] E. Rocca: "Entropic" solutions for two-phase fluids flows, phase transitions, and damage,
ISIMM -- The International Society
for the Interaction of Mechanics and Mathematics -- FORUM, March 2015.





Download here the arXiv preprints

Dowload here the WIAS preprints