Athanasios E.Tzavaras - List of Publications
Electronic files provided when available.

Books edited

1. Hyperbolic Problems: Theory, Numerics, Applications.Proceedings of HYP2008 held at the University of Maryland, College Park, June 9-13, 2008, E.Tadmor, J.-G. Liu and A.E. Tzavaras, eds; AMS Proc. Symp. Appl. Math., 2009 Vol. 67.1: Plenary & Invited Talks; Vol. 67.2: Contributed Talks.

2. Special issue: 4th international workshop on nonequilibrium thermodynamics and complex fluids. Selected papers based on the presentations at the workshop, Rhodes, Greece, Sep 3-7, 2006. (English). Mavrantzas, Vlasis G. (ed), Beris, Anthony N. (ed) and Tzavaras, Thanos (ed.) J. Non-Newton. Fluid Mech, 152, No. 1-3, 202 p. (2008).

Chapters in Books (Lecture Notes)

3. Viscosity and relaxation approximation for hyperbolic systems of conservation laws. In: An Introduction to Recent Developments in Theory and Numerics for Conservation Laws, D. Kroener, M. Ohlberger and C. Rohde, eds.; Lecture Notes in Computational Science and Engineering, Vol. 5, Springer, Berlin/Heidelberg, 1998, pp. 73-122.
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4. On the mathematical theory of fluid dynamic limits to conservation laws. In: Advances in Mathematical Fluid Mechanics, J. Malek, J. Necas and M. Rokyta, eds.;
Springer, New York, 2000, pp 192-222.
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Articles

5. Shearing of materials exhibiting thermal softening or temperature dependent viscosity. Quart. Appl. Math. 44 (1986), 1-12.

6. Plastic shearing of materials exhibiting strain hardening or strain softening. Arch. Rational Mech. Anal. 94 (1986), 39-58.

7. A quasilinear parabolic system arising in modelling of catalytic reactors (with A. Friedman). J. Differential Equations 70 (1987), 167-196.

8. Effect of thermal softening in shearing of strain-rate dependent materials. Arch. Rational Mech. Anal. 99 (1987), 349-374.

9. Combustion in a porous medium (with A. Friedman). SIAM J. Math. Anal. 19 (1988), 509-519.

10. Weak solutions for a nonlinear system in viscoelasticity (with J.A. Nohel and R.C. Rogers). Comm. Partial Differential Equations 13 (1988), 97-127.

11. Hyperbolic conservation laws in viscoelasticity (with J.A. Nohel and R.C. Rogers). In Volterra integrodifferential equations in Banach spaces and applications, G. DaPrato and M. Iannelli, eds.; Pitman Res. Notes Math. Ser., 190, Longman Sci. Tech., Harlow, 1989, pp. 320-338.

12. A limiting viscosity approach for the Riemann problem in isentropic gas dynamics (with M. Slemrod). Indiana Univ. Math. J. 38 (1989), 1047-1074.
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13. Effect of thermal softening on the response of shearing motions. In Transactions of the Seventh Army Conference on Applied Mathematics and Computing, ARO Rep., 90-1, U.S. Army Res. Office, Research Triangle Park, NC, 1990, pp 581-587.

14. Stability of discontinuous steady states in shearing motions of a non-Newtonian fluid (with J.A. Nohel and R.L. Pego). Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), 39-59.

15. Nonlinear stability in non-Newtonian flows (with J.A. Nohel and R.L. Pego). In Multidimensional hyperbolic problems and computations, J. Glimm and A. Majda, eds.; IMA Vol. Math. Appl., 29, Springer, New York, 1991, pp 251-260.

16. Strain softening in viscoelasticity of the rate type. J. Integral Equations Appl. 3 (1991), 195-238.
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17. Nonlinear analysis techniques for shear band formation at high strain-rates. Appl. Mech. Reviews 45 (1992), no.3 part 2, S82--S94.
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18. Remarks on a self-similar fluid dynamic limit for the Broadwell system (with M. Slemrod). Nonlinear kinetic theory and mathematical aspects of hyperbolic systems, C. Boffi, F. Bampi and G. Toscani, eds.; Ser. Adv. Math. Appl. Sci., 9, World Sci. Publishing, River Edge, NJ, 1992, pp 233-241,

19. Shear strain localization in plastic deformations. In Shock induced transitions and phase structures in general media, J.E. Dunn, R. Fosdick and M. Slemrod, eds.; IMA Vol. Math. Appl., 52, Springer, New York, 1993, pp 231-250.
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20. Self-similiar fluid-dynamic limits for the Broadwell system (with M. Slemrod). Arch. Rational Mech. Anal. 122 (1993), 353-392.
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21. The Broadwell system, self-similar ordinary differential equations, and fluid dynamical limits (with M. Slemrod). In Differential equations, dynamical systems, and control science, K.D. Elworthy, W.N. Everitt and E.B. Lee, eds.; Lecture Notes in Pure and Appl. Math., 152, Dekker, New York, 1994, pp 307-319.

22. Wave structure induced by fluid-dynamic limits in the Broadwell model. Arch. Rational Mech. Anal. 127 (1994), 361-387.
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23. Elastic as limit of viscoelastic response, in a context of self-similar viscous limits. J. Differential Equations 123 (1995), 305-341.
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24. Wave interactions and variation estimates for self-similar zero-viscosity limits in systems of conservation laws. Arch. Rational Mech. Anal. 135 (1996), 1-60.
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25. Shock profiles and self-similar fluid dynamic limits (with M. Slemrod). Transport Theory Statist. Phys. 25 (1996), 531-541.
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26. Existence theory for the Riemann problem for non-conservative hyperbolic systems (with Ph. LeFloch). C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 347-352.
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27. Contractive relaxation systems and interacting particles for scalar conservation laws (with M. Katsoulakis). C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 865-870.
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28. Contractive relaxation systems and the scalar multidimensional conservation law (with M. Katsoulakis). Comm. Partial Differential Equations 22 (1997), 195-233.
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29. Representation of weak limits and definition of nonconservative products (with Ph. LeFloch). SIAM J. Math. Anal. 30 (1999), 1309-1342.
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30. Multiscale analysis for interacting particles: Relaxation systems and scalar conservation laws (with M. Katsoulakis). J. Statistical Physics 96 (1999), 715-763.
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31. Materials with internal variables and relaxation to conservation laws. Arch. Rational Mech. Anal. 146 (1999), 129-155.
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32. Convergence of relaxation schemes to the equations of elastodynamics (with L. Gosse). Math. Comp. 70 (2001), 555-577.
ps - pdf - ARTICLE available at http://www.ams.org

33. Construction of entropy solutions for one dimensional elastodynamics via time discretisation (with S. Demoulini and D.M.A. Stuart). Annales de l'I.H.P. Anal. Nonlineaire, 17 (2000), 711-731.
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34. Kinetic formulation for systems of two conservation laws and elastodynamics (with B. Perthame). Arch. Rational Mech. Analysis 155 (2000), 1-48.
ps - pdf - ARTICLE available at http://www.springerlink.com

35. A variational approximation scheme for three-dimensional elastodynamics with polyconvex energy (with S. Demoulini and D.M.A. Stuart). Arch. Rational Mech. Analysis, 157 (2001), 325-344.
ps - pdf - ARTICLE available at http://www.springerlink.com

36. Diffusive N-waves and metastability in the Burgers equation (with Y.-J. Kim). SIAM J. Math. Analysis 33 (2001), 607-633.
ps - pdf - ARTICLE available at http://epubs.siam.org

37. Kinetic decomposition of approximate solutions to conservation laws: applications to relaxation and diffusion-dispersion approximations (with S. Hwang). Comm. PDE 27 (2002), 1229-1254.
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38. Derivation of fluid equations for kinetic models with one conserved quantity. In Proceedings of International Conference on Mathematical Analysis, National Technical Univ. of Athens, Greece, 2003.
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39. $L^1$ stability for the one-dimensional Broadwell model of a discrete velocity gas (with S.-Y. Ha). In Hyperbolic Problems: Theory, Numerics and Applications, T. Hou and E. Tadmor, eds.; Springer, New York, 2003, pp. 205-215.
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40. Lyapunov functionals and $L^1$ stability for discrete velocity Boltzmann equations (with S.-Y. Ha). Comm. Math. Physics 239 (2003), 65-92.
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41. The Riemann function, singular entropies, and the structure of oscillations in systems of two conservation laws. Arch. Rational Mech. Anal., 169 (2003), 119-145.
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42. Stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws (with Ch. Arvanitis and Ch. Makridakis). SIAM J. Numer. Analysis 42 (2004), 1357-1393.
ps - pdf - ARTICLE available at http://epubs.siam.org

43. Relative entropy in hyperbolic relaxation. Comm. Math. Sci. 3 (2005), 119-132.
ps - pdf - ARTICLE available at http://intlpress.com/CMS

44. Structural properties of stress relaxation and convergence from viscoelasticity to polyconvex elastodynamics (with C. Lattanzio). Arch. Rational Mech. Anal., 180 (2006), 449-492.
ps - pdf - ARTICLE available at http://www.springerlink.com

45. A finite element method for computing shear band formation (with Th. Baxevanis, Th. Katsaounis). In Proceedings of the 10th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2004), Vol. I, F. Asakura et al, eds; Yokohama Publishers, Osaka, 2006, pp. 295-302.
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46. Hydrodynamic limits for kinetic equations and the diffusive approximation of radiative transport for accoustic waves (with M. Portilheiro). Transactions Amer. Math. Soc. 359 (2007), 529-565.
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47. Continuity of velocity gradients in suspensions of rod-like molecules (with F. Otto). Comm. Math. Physics 277 (2008), 729-758.
ps - pdf - ARTICLE available at http://www.springerlink.com

48. Kinetic decomposition for periodic homogenization problems (with P.-E. Jabin). SIAM J. Math. Anal. 41 (2009), 360-390.
pdf - ARTICLE available at SIAM Journals online

49. Effective equations for localization and shear band formation (with Th. Katsaounis). SIAM J. Appl. Math. 69 (2009), 1618-1643.
pdf - ARTICLE available at SIAM Journals online

50. Kinetic hierarchies and macroscopic limits for crystalline steps in 1+1 dimension (with D. Margetis). Multiscale Model. Simul. 7 (2009), 1428-1454.
pdf - ARTICLE available at SIAM journals online

51. From discrete velocity Boltzmann equations to gas dynamics before shocks (with F. Berthelin and A. Vasseur). J. Stat. Physics 135 (2009), 151-173.
pdf - ARTICLE available from springerlink.com

52. Adaptive finite element computations of shear band formation (with Th. Baxevanis and Th. Katsaounis). Math. Models Methods Applied Sciences 20 (2010), 423-448.
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53. Localization and shear bands in high strain-rate plasticity (with Th. Katsaounis). In Nonlinear Conservation Laws and Applications , A. Bressan, G.-Q. Chen, M. Lewicka and D. Wang, eds; IMA Vol. Math. Appl., 153, Springer, New York, 2011, pp 365-378.
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54. A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians (with A. Miroshnikov). Comm. Math. Sciences 10 (2012), 87-115.
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55. Remarks on the contributions of Constantine M. Dafermos to the subject of Conservation Laws (with G.-Q. Chen) Acta Math. Scientia 32B (2012), 3-14.
pdf - ARTICLE available at http://www.sciencedirect.com

56. Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics (with S. Demoulini and D.M.A. Stuart). Arch. Rational Mech. Analysis 205 (2012), 927-961.
pdf - ARTICLE available from springerlink.com

57. Relative entropy in diffusive relaxation (with C. Lattanzio). SIAM J. Math. Analysis 45 (2013), 1563-1584.
pdf - ARTICLE available at SIAM Journals online

58. The problem of dynamic cavitation in nonlinear elasticity (with J. Giesselmann, A. Miroshnikov). Seminaire Laurent Schwartz - EDP et applications (2012-2013), Exp No. 14, 17p.
pdf - ARTICLE available from cedram.org

59. Stress relaxation models with polyconvex entropy in Lagrangean and Eulerian coordinates. Comm. in Information and Systems 13 (2014), 43-64.
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60. Relative entropy methods for hyperbolic and diffusive limits (with C. Lattanzio). In Hyperbolic Problems: Theory, Numerics, Applications, F. Ancona, A. Bressan, P. Marcati, A. Marson, eds; AIMS Series on Applied Mathematics, Vol 8, Springfield, 2014, pp. 163-177.
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61. Convergence of variational approximation schemes for three dimensional elastodynamims with polyconvex energy (with A. Miroshnikov). J. Analysis Appl. (ZAA) 33 (2014), 43-64.
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62. On cavitation in nonlinear elastodynamics (with J. Giesselmann). In Hyperbolic Problems: Theory, Numerics, Applications, F. Ancona, A. Bressan, P. Marcati, A. Marson, eds; AIMS Series on Applied Mathematics, Vol 8, Springfield, 2014, pp. 599-606.
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63. Singular limiting induced from continuum solutions and the problem of dynamic cavitation (with J. Giesselmann). Arch. Rational Mech. Analysis 212 (2014), 241-281.
pdf - ARTICLE available from springerlink.com

64. On the construction and properties of weak solutions describing dynamic cavitation (with A. Miroshnikov). J. Elasticity 118 (2015), 141-185.
pdf - ARTICLE available from springerlink.com

65. A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows (with Ch. Helzel). Physica D 337 (2016), 18-29.
pdf -- ARTICLE available at http://www.sciencedirect.com

66. Localization in inelastic rate dependent shearing deformations (with Th. Katsaounis and Min-Gi Lee). J. Mech. Physics Solids 98 (2017), 106-125.
pdf -- ARTICLE available at http://www.sciencedirect.com

67. Relative energy for the Korteweg-theory and related Hamiltonian flows in gas dynamics (with J. Giesselmann and C. Lattanzio). Arch. Rational Mech. Analysis 223 (2017), 1427-1484.
pdf - ARTICLE available from springerlink.com

68. Emergence of coherent localized structures in shear deformations of temperature dependent fluids (with J. Olivier, Th. Katsaounis). Arch. Rational Mech. Analysis 224 (2017), 173-208.
pdf - ARTICLE available from springerlink.com

69. Existence of localizing solutions in plasticity via geometric theory of singular perturbations (with Min-Gi Lee). SIAM J. Appl. Dyn. Syst. 16 (2017), 337-360.
pdf - ARTICLE available at SIAM Journals online

70. From gas dynamics with large friction to gradient flows describing diffusion theories (with C. Lattanzio). Comm. Partial Differential Equations 42 (2017), 261-290.
pdf -- ARTICLE available from Taylor and Francis online

71. A kinetic model for the sedimentation of rod-like particles (with Ch. Helzel). Multiscale Model. Simul. 15 (2017), 500-536.
pdf - ARTICLE available at SIAM Journals online

72. Stability properties of the Euler-Korteweg system with nonmonotone pressures (with Jan Giesselmann). Applicable Anal. 96 (2017), 1528-1546.
pdf -- ARTICLE available from Taylor and Francis online

73. Th. Katsaounis, K. Kotsovos, I. Gereige, A. Al-Saggaf and A. Tzavaras. 2D simulation and performance evaluation of bifacial high efficiency c-Si solar cells under variable illumination conditions. Solar Energy 158 (2017), 34-41.
pdf -- ARTICLE available from ScienceDirect

74. Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity (with C. Christoforou). Arch. Rational Mech. Analysis 229 (2018), 1-52.
pdf - ARTICLE available from springerlink.com

75. M.~G. Lee, Th. Katsaounis and A.E. Tzavaras, Localization of adiabatic deformations in thermoviscoplastic materials. In <\em> Theory, Numerics and Applications of Hyperbolic Problems II, Ch. Klingenberg and M. Westdickenberg, eds; Springer Proceedings in Mathematics & Statistics, Vol 237, Springer, Berlin, 2018, pp .
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76. On the relative entropy method for hyperbolic-parabolic systems (with Cl. Christoforou). In <\em> Theory, Numerics and Applications of Hyperbolic Problems II, Ch. Klingenberg and M. Westdickenberg, eds; Springer Proceedings in Mathematics & Statistics, Vol 237, Springer, Berlin, 2018, pp .
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77. A symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniqueness (with Cl. Christoforou and M. Galanopoulou). Comm. Partial Differential Equations (in press).
pdf -- ARTICLE available from Taylor and Francis online

Preprints

78. M.~G. Lee, Th. Katsaounis and A.E. Tzavaras Localization in adiabatic shear flow via geometric theory of singular perturbations.
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79. Conservation of energy for the Euler-Korteweg equations (with Tomasz Debiec, Piotr Gwiazda and Agnieszka Swierczewska-Gwiazda)
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