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

    Contributions in Books (Lecture Notes)

  1. 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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  2. 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

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

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

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

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

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

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

  9. 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.

  10. A limiting viscosity approach for the Riemann problem in isentropic gas dynamics (with M. Slemrod). Indiana Univ. Math. J. 38 (1989), 1047-1074.

  11. 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.

  12. 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.

  13. 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.

  14. Strain softening in viscoelasticity of the rate type. J. Integral Equations Appl. 3 (1991), 195-238.
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  15. 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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  16. 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,

  17. 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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  18. Self-similiar fluid-dynamic limits for the Broadwell system (with M. Slemrod). Arch. Rational Mech. Anal. 122 (1993), 353-392.
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  19. 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.

  20. Wave structure induced by fluid-dynamic limits in the Broadwell model. Arch. Rational Mech. Anal. 127 (1994), 361-387.
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  21. 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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  22. Wave interactions and variation estimates for self-similar zero-viscosity limits in systems of conservation laws. Arch. Rational Mech. Anal. 135 (1996), 1-60.
    - ps - pdf - ARTICLE available at http://www.springerlink.com

  23. Shock profiles and self-similar fluid dynamic limits (with M. Slemrod). Transport Theory Statist. Phys. 25 (1996), 531-541.
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  24. 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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  25. 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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  26. Contractive relaxation systems and the scalar multidimensional conservation law (with M. Katsoulakis). Comm. Partial Differential Equations 22 (1997), 195-233.
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  27. Representation of weak limits and definition of nonconservative products (with Ph. LeFloch). SIAM J. Math. Anal. 30 (1999), 1309-1342.
    ps - pdf - ARTICLE available at http://epubs.siam.org

  28. 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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  29. Materials with internal variables and relaxation to conservation laws. Arch. Rational Mech. Anal. 146 (1999), 129-155.
    ps - pdf - ARTICLE available at http://www.springerlink.com

  30. 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

  31. 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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  32. 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

  33. 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

  34. 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

  35. 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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  36. 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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  37. $L^1$ 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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  38. Lyapunov functionals and $L^1$ stability for discrete velocity Boltzmann equations (with S.-Y. Ha). Comm. Math. Physics 239 (2003), 65-92.
    ps - pdf - ARTICLE available at http://www.springerlink.com

  39. The Riemann function, singular entropies, and the structure of oscillations in systems of two conservation laws. Arch. Rational Mech. Anal., 169 (2003), 119-145.
    ps - pdf - ARTICLE available at http://www.springerlink.com

  40. 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

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

  42. 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

  43. 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.
    ps - pdf - ARTICLE available at http://www.ams.org/tran

  44. 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

  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. A relaxation theory with polyconvex entropy function converging to elastodynamics
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  47. 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

  48. 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

  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. 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

  51. Adaptive finite element computations of shear band formation (with Th. Baxevanis and Th. Katsaounis). Math. Models Methods Applied Sciences (to appear).
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