• F. Berthelin, A.E. Tzavaras and A. Vasseur
  From discrete velocity Boltzmann equations to gas dynamics before shocks
  pdf - ps
  
  
• Th. Baxevanis, Th. Katsaounis and A.E. Tzavaras
  Adaptive finite element computations of shear band formation
  pdf (6.6 MB)
  
  
• Th. Katsaounis and A.E. Tzavaras
  Effective equations for localization and shear band formation
  pdf
  
  
• D. Margetis and A.E. Tzavaras
  Kinetic hierarchies and macroscopic limits for crystalline steps in 1+1 dimension
  pdf
  
  
• P.-E. Jabin and A.E. Tzavaras
  Kinetic decomposition for periodic homogenization problems
  ps - pdf
  
  
• A. Tzavaras
  A relaxation theory with polyconvex entropy function converging to elastodynamics
  ps - pdf
  
  

• Review Articles - Lecture Notes
  
  
• Kinetic Theory
  
  • Relaxation and Hydrodynamic limits
    
  • Particle systems
    
  • Discrete velocity models
    
  • Polymers - Material Science
    
  
  
• Nonlinear Dynamics of Continuous Media
  
  • Nonlinear elastodynamics and viscoelasticity
    
  • Shear bands
    
  • Phase transitions in viscoelasticity
    
  
  
• Hyperbolic Conservation Laws
  
  • Effect of diffusion on dynamics
    
  • Self-similar zero-viscosity limits
    
  • Relaxation and Hydrodynamic limits
    
  • Conservation laws with memory
    
  • Numerical methods
    
  
  
• Reaction-Diffusion Problems - Parabolic Systems
  

• A.E. Tzavaras (1992)
  Nonlinear analysis techniques for shear band formation at high strain-rates
  Appl. Mech. Reviews 45 (1992), no.3 part 2, S82--S94. - ps
  
  
• A.E. Tzavaras (1998)
  Viscosity and relaxation approximation for hyperbolic systems of conservation laws
  Lecture Notes from the "International School on Theory and Numerics for Conservation Laws", Freiburg, Germany, Oct. 1997.
  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. - abstract - ps - pdf
  
  
• A. Tzavaras (2000)
  On the mathematical theory of fluid dynamic limits to conservation laws
  Lecture Notes from the Sixth School on "Mathematical Theory in Fluid Mechanics", at Paseky of Czech Republic, Oct 99.
  In: Advances in Mathematical Fluid Mechanics, J. Malek, J. Necas and M. Rokyta, eds.;
  Springer, New York, 2000, pp 192-222. - ps - pdf
  
  

Relaxation and Hydrodynamic limits

• M. Katsoulakis and A.E. Tzavaras (1997)
  Contractive relaxation systems and the scalar multidimensional conservation law
  Comm. Partial Differential Equations 22 (1997), 195-233. - ps
  
  
• A.E. Tzavaras (1999)
  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
  
  
• B. Perthame and A.E. Tzavaras (2000)
  Kinetic formulation for systems of two conservation laws and elastodynamics
  Arch. Rational Mech. Analysis 155 (2000), 1-48.
  - ps - pdf - ARTICLE available at http://www.springerlink.com
  
  
• S. Hwang and A. Tzavaras (2002)
  Kinetic decomposition of approximate solutions to conservation laws:
  applications to relaxation and diffusion-dispersion approximations
  Comm. PDE 27 (2002), 1229-1254. - ps - pdf
  
  
• A. Tzavaras (2003)
  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.
  ps - pdf
  
  
• S. Hwang (2003)
  Kinetic decomposition for kinetic models of BGK type
  Journal of Differential Equations, 130 (2003), 353-363. - ps
  
  
• A. Tzavaras (2003)
  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
  
  
• A.E. Tzavaras (2005)
  Relative entropy in hyperbolic relaxation
  Comm. Math. Sci. 3 (2005), 119-132.
  ps - pdf - ARTICLE available at http://intlpress.com/CMS
  
  
• M. Portilheiro and A. Tzavaras (2007)
  Hydrodynamic limits for kinetic equations and the diffusive approximation of radiative transport for accoustic waves
  Transactions Amer. Math. Soc. 359 (2007), 529-565.
  ps - pdf - ARTICLE available at http://www.ams.org/tran
  
  
• [ See also ]

Particle systems

• M. Katsoulakis and A.E. Tzavaras (1996)
  Contractive relaxation systems and interacting particles for scalar conservation laws
  C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 865-870. - ps
  
  
• M. Katsoulakis and A.E. Tzavaras (1999)
  Multiscale analysis for interacting particles: Relaxation systems and scalar conservation laws
  J. Statistical Physics 96 (1999), 715-763. - ps - pdf
  
  

Discrete velocity models

• M. Slemrod and A.E. Tzavaras (1992)
  Remarks on a self-similar fluid dynamic limit for the Broadwell system
  In 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,
  
  
• M. Slemrod and A.E. Tzavaras (1993)
  Self-similar fluid-dynamic limits for the Broadwell system
  Arch. Rational Mech. Anal. 122 (1993), 353-392. - ps
  
  
• M. Slemrod and A.E. Tzavaras (1994)
  The Broadwell system, self-similar ordinary differential equations, and fluid dynamical limits
  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.
  
  
• A.E. Tzavaras (1994)
  Wave structure induced by fluid-dynamic limits in the Broadwell model.
  Arch. Rational Mech. Anal. 127 (1994), 361-387. - ps
  
  
• M. Slemrod and A.E. Tzavaras (1996)
  Shock profiles and self-similar fluid dynamic limits
  Transport Theory Statist. Phys. 25 (1996), 531-541. - ps
  
  
• S.-Y. Ha and A. Tzavaras (2003)
  Lyapunov functionals and $L^1$ stability for discrete velocity Boltzmann equations
  Comm. Math. Physics 239 (2003), 65-92.
  - ps - pdf - ARTICLE available at http://www.springerlink.com
  
  
• S.-Y. Ha and A. Tzavaras (2003)
  $L^1$ stability for the one-dimensional Broadwell model of a discrete velocity gas
  In Hyperbolic Problems: Theory, Numerics and Applications, T. Hou and E. Tadmor, eds.; Springer, New York, 2003, pp. 205-215.
  ps - pdf
  
  

Polymers - Material Science

• F. Otto and A. Tzavaras (2008)
  Continuity of velocity gradients in suspensions of rod-like molecules
  ps - pdf - ARTICLE available at http://www.springerlink.com
  
  

Nonlinear elastodynamics and viscoelasticity

• S. Demoulini, D. Stuart and A. Tzavaras (2000)
  Construction of entropy solutions for one dimensional elastodynamics via time discretisation
  Annales de l'I.H.P. Anal. Nonlineaire, 17 (2000), 711-731. - ps - pdf
  
  
• S. Demoulini, D. Stuart and A. Tzavaras (2001)
  A variational approximation scheme for three-dimensional elastodynamics with polyconvex energy
  Arch. Rational Mech. Analysis, 157 (2001), 325-344.
  - ps - pdf - ARTICLE available at http://www.springerlink.com
  
  
• C. Lattanzio and A.E. Tzavaras (2006)
  Structural properties of stress relaxation and convergence from viscoelasticity to polyconvex elastodynamics Arch. Rational Mech. Anal., 180 (2006), 449-492.
  ps - pdf - ARTICLE available at http://www.springerlink.com
  
  

Shear bands

• A.E. Tzavaras (1986)
  Shearing of materials exhibiting thermal softening or temperature dependent viscosity
  Quart. Appl. Math. 44 (1986), 1-12.
  
  
• A.E. Tzavaras (1986)
  Plastic shearing of materials exhibiting strain hardening or strain softening
  Arch. Rational Mech. Anal. 94 (1986), 39-58.
  
  
• A.E. Tzavaras (1987)
  Effect of thermal softening in shearing of strain-rate dependent materials
  Arch. Rational Mech. Anal. 99 (1987), 349-374.
  
  
• A.E. Tzavaras (1990)
  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.
  
  
• A.E. Tzavaras (1991)
  Strain softening in viscoelasticity of the rate type
  J. Integral Equations Appl. 3 (1991), 195-238. - ps
  
  
• A.E. Tzavaras (1992)
  Nonlinear analysis techniques for shear band formation at high strain-rates
  Appl. Mech. Reviews 45 (1992), no.3 part 2, S82--S94. - ps
  
  
• A.E. Tzavaras (1993)
  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. - ps
  
  
• Th. Baxevanis, Th. Katsaounis and A.E. Tzavaras (2006)
  A finite element method for computing shear band formation
  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.
  ps - pdf
  
  

Phase transitions in viscoelasticity

• J.A. Nohel, R.L. Pego and A.E. Tzavaras (1990)
  Stability of discontinuous steady states in shearing motions of a non-Newtonian fluid
  Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), 39-59.
  
  
• J.A. Nohel, R.L. Pego and A.E. Tzavaras (1991)
  Nonlinear stability in non-Newtonian flows
  In Multidimensional hyperbolic problems and computations, J. Glimm and A. Majda, eds.; IMA Vol. Math. Appl., 29, Springer, New York, 1991, pp 251-260.
  
  
• F. Otto and A. Tzavaras (2008)
  Continuity of velocity gradients in suspensions of rod-like molecules
  ps - pdf - ARTICLE available at http://www.springerlink.com
  
  

Effect of diffusion on dynamics

• Ph. LeFloch and A.E. Tzavaras (1996)
  Existence theory for the Riemann problem for non-conservative hyperbolic systems
  C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 347-352. - ps
  
  
• Ph. LeFloch and A.E. Tzavaras (1999)
  Representation of weak limits and definition of nonconservative products
  SIAM J. Math. Anal. 30 (1999), 1309-1342.
  - ps - pdf - ARTICLE available at http://epubs.siam.org
  
  
• Y.-J. Kim and A.E. Tzavaras (2001)
  Diffusive N-waves and metastability in the Burgers equation
  SIAM J. Math. Analysis 33 (2001), 607-633.
  - ps - pdf - ARTICLE available at http://epubs.siam.org
  
  

Self-similar zero-viscosity limits

• M. Slemrod and A.E. Tzavaras (1989)
  A limiting viscosity approach for the Riemann problem in isentropic gas dynamics
  Indiana Univ. Math. J. 38 (1989), 1047-1074.
  
  
• A.E. Tzavaras (1995)
  Elastic as limit of viscoelastic response, in a context of self-similar viscous limits
  J. Differential Equations 123 (1995), 305-341. - ps
  
  
• A.E. Tzavaras (1996)
  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
  
  
• Y.J. Kim (2001)
  A self-similar viscosity approach for the Riemann problem in isentropic gas dynamics and the structure of the solutions
  Quart. Applied Math. 59 (2001), 637-665. - ps
  
  
• [ See also ]

Relaxation and Hydrodynamic limits - [ Go to ]

Conservation laws with memory

Numerical methods

• L. Gosse and A.E. Tzavaras (2001)
  Convergence of relaxation schemes to the equations of elastodynamics
  Math. Comp. 70 (2001), 555-577.
  - ps - pdf - ARTICLE available at http://www.ams.org
  
  
• Ch. Arvanitis, Ch. Makridakis and A. Tzavaras (2004)
  Stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws
  SIAM J. Numer. Analysis 42 (2004), 1357-1393.
  ps - pdf - ARTICLE available at http://epubs.siam.org