A.E. Tzavaras, Nonlinear analysis techniques for shear band formation at high strain-rates. Appl. Mech. Reviews 45 (1992), no.3 part 2, S82--S94. pdf
A.E. Tzavaras, 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. 73-12, pdf
A.E. Tzavaras, 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. pdf
G.-Q. Chen and A.E. Tzavaras, Remarks on the contributions of Constantine M. Dafermos to the subject of Conservation Laws, Acta Math. Scientia 32B (2012), 3-14. pdf - ARTICLE available at http://www.sciencedirect.com
J. Giesselmann, A. Miroshnikov and A.E. Tzavaras, The problem of dynamic cavitation in nonlinear elasticity, Seminaire Laurent Schwartz - EDP et applications (2012-2013), Exp No. 14, 17p. pdf - ARTICLE available from cedram.org
B. Perthame and A.E. Tzavaras, Kinetic formulation for systems of two conservation laws and elastodynamics, Arch. Rational Mech. Analysis 155 (2000), 1-48. pdf - ARTICLE available at http://www.springerlink.com
S. Hwang and A. Tzavaras, Kinetic decomposition of approximate solutions to conservation laws: applications to relaxation and diffusion-dispersion approximations, Comm. PDE 27 (2002), 1229-1254. pdf
A. Tzavaras, The Riemann function, singular entropies, and the structure of oscillations in systems of two conservation laws. Arch. Rational Mech. Anal., 169 (2003), 119-145. pdf - ARTICLE available at http://www.springerlink.com
P.-E. Jabin and A.E. Tzavaras, Kinetic decomposition for periodic homogenization problems, SIAM J. Math. Anal. 41 (2009), 360-390. pdf - ARTICLE available at SIAM Journals online
Athanasios E. Tzavaras, Sustained oscillations in hyperbolic-parabolic systems (2023). pdf
Daria Bolbot, Dimitrios Mitsotakis and A.E. Tzavaras. Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics. Quart. Appl. Math. 81 (3) (2023), 455-481. pdf - ARTICLE available from AMS -
Larkspur Brudvik-Lindner, Dimitrios Mitsotakis and A.E. Tzavaras. Oscillatory and regularized shock waves for a dissipative Peregrine-Boussinesq system. IMA J. Appl. Math. 88 (2023), 602-631. pdf-article available from Oxford Univ. Press
M. Katsoulakis and A.E. Tzavaras, Contractive relaxation systems and the scalar multidimensional conservation law, Comm. Partial Differential Equations 22 (1997), 195-233. - pdf
A.E. Tzavaras, Materials with internal variables and relaxation to conservation laws, Arch. Rational Mech. Anal. 146 (1999), 129-155. pdf - ARTICLE available at http://www.springerlink.com
A. Tzavaras, 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. pdf
S. Hwang, A. Tzavaras, Kinetic decomposition for kinetic models of BGK type, Journal of Differential Equations, 130 (2003), 353-363. pdf
A.E. Tzavaras, Relative entropy in hyperbolic relaxation, Comm. Math. Sci. 3 (2005), 119-132. pdf - ARTICLE available at http://intlpress.com/CMS
M. Portilheiro and A. Tzavaras, Hydrodynamic limits for kinetic equations and the diffusive approximation of radiative transport for accoustic waves, Transactions Amer. Math. Soc. 359 (2007), 529-565. pdf - ARTICLE available at http://www.ams.org/tran
C. Lattanzio and A.E. Tzavaras, Relative entropy methods for hyperbolic and diffusive limits, In Hyperbolic Problems: Theory, Numerics, Applications(HYP2012), F. Ancona, A. Bressan, P. Marcati, A. Marson, eds; AIMS Series on Applied Mathematics, Vol 8, Springfield, 2014, pp. 163-177. pdf
Nuno J. Alves and A.E. Tzavaras. The relaxation limit of bipolar fluid models. Discrete Cont. Dynam. Systems 42 (1) (2022), 211-237. pdf - ARTICLE available from AIMS
M. Katsoulakis and A.E. Tzavaras, Contractive relaxation systems and interacting particles for scalar conservation laws, C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 865-870. pdf
M. Katsoulakis and A.E. Tzavaras, Multiscale analysis for interacting particles: Relaxation systems and scalar conservation laws, J. Statistical Physics 96 (1999), 715-763. pdf
M. Slemrod and A.E. Tzavaras, 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, Self-similar fluid-dynamic limits for the Broadwell system, Arch. Rational Mech. Anal. 122 (1993), 353-392. pdf
M. Slemrod and A.E. Tzavaras, 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, Wave structure induced by fluid-dynamic limits in the Broadwell model, Arch. Rational Mech. Anal. 127 (1994), 361-387. pdf
M. Slemrod and A.E. Tzavaras, Shock profiles and self-similar fluid dynamic limits, Transport Theory Statist. Phys. 25 (1996), 531-541. pdf
S.-Y. Ha and A. Tzavaras, Lyapunov functionals and $L^1$ stability for discrete velocity Boltzmann equations, Comm. Math. Physics 239 (2003), 65-92. pdf - ARTICLE available at http://www.springerlink.com
S.-Y. Ha and A. Tzavaras, $L^1$ 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. pdf
F. Berthelin, A.E. Tzavaras and A. Vasseur, From discrete velocity Boltzmann equations to gas dynamics before shocks, J. Stat. Physics 135 (2009), 151-173. pdf - ARTICLE available from springerlink.com
F. Otto and A. Tzavaras, Continuity of velocity gradients in suspensions of rod-like molecules, Comm. Math. Physics 277 (2008), 729-758. pdf - ARTICLE available at http://www.springerlink.com
D. Margetis and A.E. Tzavaras, Kinetic hierarchies and macroscopic limits for crystalline steps in 1+1 dimension, Multiscale Model. Simul. 7 (2009), 1428-1454. pdf - ARTICLE available at SIAM journals online
Ch. Helzel and A.E. Tzavaras (2016), A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows, Physica D 337 (2016), 18-29. pdf -- ARTICLE available at http://www.sciencedirect.com
Ch. Helzel and A.E. Tzavaras (2017), A kinetic model for the sedimentation of rod-like particles, Multiscale Model. Simul. 15 (2017), 500-536. pdf - ARTICLE available at SIAM Journals online-- an earlier version preprint (Oct 2010)
C. Lattanzio and A.E. Tzavaras, Relative entropy in diffusive relaxation, SIAM J. Math. Analysis 45 (2013), 1563-1584. pdf - ARTICLE available at SIAM Journals online
J. Giesselmann, C. Lattanzio and A. Tzavaras, Relative energy for the Korteweg-theory and related Hamiltonian flows in gas dynamics, Arch. Rational Mech. Analysis 223 (2017), 1427-1484. pdf - ARTICLE available from springerlink.com
C. Lattanzio and A. Tzavaras, From gas dynamics with large friction to gradient flows describing diffusion theories, Comm. Partial Differential Equations 42 (2017), 261-290. pdf -- ARTICLE available from Taylor and Francis online
Jan Giesselmann and Athanasios E. Tzavaras, Stability properties of the Euler-Korteweg system with nonmonotone pressures, Applicable Anal. 96 (2017), 1528-1546. pdf -- ARTICLE available from Taylor and Francis online
Tomasz Debiec, Piotr Gwiazda, Agnieszka Swierczewska-Gwiazda and Athanasios E. Tzavaras, Conservation of energy for the Euler-Korteweg equations. Calc. Variations PDE 57 (2018):160. pdf - ARTICLE available from springerlink.com
Xiaokai Huo, Ansgar Juengel and A.E. Tzavaras, High-friction limits of Euler flows for multicomponent systems. Nonlinearity 32 (2019), 2875-2913. pdf - ARTICLE available from IOP Science
Nuno J. Alves and A.E. Tzavaras. The relaxation limit of bipolar fluid models. Discrete Cont. Dynam. Systems 42 (1) (2022), 211-237. pdf - ARTICLE available from AIMS
Nuno Alves and A.E. Tzavaras, Zero-electron-mass and quasi-neutral limits for bipolar Euler-Poisson systems. Z. Angew. Math. Phys. 75 (2024): Art 17, 19 pp. pdf - ARTICLE available from springerlink.com
S. Demoulini, D. Stuart and A. Tzavaras, Construction of entropy solutions for one dimensional elastodynamics via time discretisation, Annales de l'I.H.P. Anal. Nonlineaire, 17 (2000), 711-731. pdf
S. Demoulini, D. Stuart and A. Tzavaras, A variational approximation scheme for three-dimensional elastodynamics with polyconvex energy, Arch. Rational Mech. Analysis, 157 (2001), 325-344. pdf - ARTICLE available at http://www.springerlink.com
C. Lattanzio and A.E. Tzavaras, Structural properties of stress relaxation and convergence from viscoelasticity to polyconvex elastodynamics, Arch. Rational Mech. Anal., 180 (2006), 449-492. pdf - ARTICLE available at http://www.springerlink.com
A. Tzavaras, A relaxation theory with polyconvex entropy function converging to elastodynamics (unpublished). pdf
A. Tzavaras, Stress relaxation models with polyconvex entropy in Lagrangean and Eulerian coordinates. Comm. in Information and Systems 13 (2014), 43-64. pdf
A. Miroshnikov and A.E. Tzavaras, A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians, Comm. Math. Sciences 10 (2012), 87-115. pdf - ARTICLE available at www.intlpress.com
S. Demoulini, D.M.A. Stuart and A.E. Tzavaras, Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics, Arch. Rational Mech. Analysis 205 (2012), 927-961. pdf - ARTICLE available from springerlink.com
A. Miroshnikov and A.E. Tzavaras, Convergence of variational approximation schemes for three dimensional elastodynamics with polyconvex energy, J. Anal. Appl. (ZAA) 33 (2014), 43-64. pdf
K. Koumatos, C. Lattanzio, S. Spirito and A.E. Tzavaras, Existence and uniqueness of a viscoelastic Kelvin-Voigt model with nonconvex stored energy. J. Hyperbolic Diff. Equations 44 (2) (2023), 433-474. pdf-article available from WorldScientific
J. Giesselmann and A.E. Tzavaras, Singular limiting induced from continuum solutions and the problem of dynamic cavitation, Arch. Rational Mech. Analysis 212 (2014), 241-281. pdf - ARTICLE available from springerlink.com
A. Miroshnikov and A.E. Tzavaras, On the construction and properties of weak solutions describing dynamic cavitation, J. Elasticity 118 (2015), 141-185. pdf - ARTICLE available from springerlink.com
J. Giesselmann and A.E. Tzavaras, On cavitation in nonlinear elastodynamics, 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. pdf
J. Giesselmann, A. Miroshnikov and A.E. Tzavaras, The problem of dynamic cavitation in nonlinear elasticity, Seminaire Laurent Schwartz - EDP et applications (2012-2013), Exp No. 14, 17p. pdf - ARTICLE available from cedram.org
A.E. Tzavaras, Shearing of materials exhibiting thermal softening or temperature dependent viscosity, Quart. Appl. Math. 44 (1986), 1-12. ARTICLE at Journal site
A.E. Tzavaras, Plastic shearing of materials exhibiting strain hardening or strain softening, Arch. Rational Mech. Anal. 94 (1986), 39-58. ARTICLE at Journal site
A.E. Tzavaras, Effect of thermal softening in shearing of strain-rate dependent materials, Arch. Rational Mech. Anal. 99 (1987), 349-374. ARTICLE at Journal site
A.E. Tzavaras, 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, Strain softening in viscoelasticity of the rate type, J. Integral Equations Appl. 3 (1991), 195-238. pdf
A.E. Tzavaras, Nonlinear analysis techniques for shear band formation at high strain-rates, Appl. Mech. Reviews 45 (1992), no.3 part 2, S82--S94. pdf
A.E. Tzavaras, 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. pdf
Th. Baxevanis, Th. Katsaounis and A.E. Tzavaras, 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. pdf
Th. Katsaounis and A.E. Tzavaras, Effective equations for localization and shear band formation, SIAM J. Appl. Math. 69 (2009), 1618-1643. pdf - ARTICLE available at SIAM Journals online
Th. Baxevanis, Th. Katsaounis and A.E. Tzavaras, Adaptive finite element computations of shear band formation, Math. Models Methods Applied Sciences 20 (2010), 423-448. pdf (6.6 MB)
Th. Katsaounis and A.E. Tzavaras, Localization and shear bands in high strain-rate plasticity, 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. pdf
J. Olivier, Th. Katsaounis and A.E. Tzavaras, Emergence of coherent localized structures in shear deformations of temperature dependent fluids, Arch. Rational Mech. Analysis 224 (2017), 173-208. pdf - ARTICLE available from springerlink.com
Th. Katsaounis, Min-Gi Lee and Athanasios Tzavaras, Localization in inelastic rate dependent shearing deformations, J. Mech. Physics Solids 98 (2017), 106-125. pdf -- ARTICLE available at http://www.sciencedirect.com
Min-Gi Lee and Athanasios Tzavaras, Existence of localizing solutions in plasticity via geometric theory of singular perturbations, SIAM J. Appl. Dyn. Syst. 16 (2017), 337-360. pdf - ARTICLE available at SIAM Journals online
M-G. Lee, Th. Katsaounis and A.E. Tzavaras, Localization of adiabatic deformations in thermoviscoplastic materials, In 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 269-280. pdf
M-G. Lee, Th. Katsaounis and A.E. Tzavaras. Localization in adiabatic shear flow via geometric theory of singular perturbations. J. Nonlinear Science 29 (2019), 2055-2101. pdf - ARTICLE available from springerlink.com
J.A. Nohel, R.L. Pego and A.E. Tzavaras, 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, 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. ARTICLE at Journal site
F. Otto and A. Tzavaras, Continuity of velocity gradients in suspensions of rod-like molecules, Comm. Math. Physics 277 (2008), 729-758. pdf - ARTICLE available at http://www.springerlink.com
C. Christoforou and A. Tzavaras, Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity, Arch. Rational Mech. Analysis 229 (2018), 1-52. pdf - ARTICLE available from springerlink.com
C. Christoforou and A. Tzavaras, On the relative entropy method for hyperbolic-parabolic systems. In Theory, Numerics and Applications of Hyperbolic Problems I, Ch. Klingenberg and M. Westdickenberg, eds; Springer Proceedings in Mathematics & Statistics, Vol 236, Springer, Berlin, 2018, pp 363-374. pdf
Cleopatra Christoforou, Myrto Galanopoulou and A.E. Tzavaras, A symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniqueness. Comm. Partial Differential Equations 43 (2018), 1019-1050. pdf -- ARTICLE available from Taylor and Francis online
Cleopatra Christoforou, Myrto Galanopoulou and A.E. Tzavaras, Measure-valued solutions for the equations of adiabatic polyconvex thermoelasticity. Discrete Cont. Dynam. Systems 39 (2019), 6175-6206. pdf - ARTICLE available from AIMS Sciences
Cleopatra Christoforou, Myrto Galanopoulou and A.E. Tzavaras, A discrete variational scheme for isentropic processes in polyconvex thermoelasticity. Calc. Variations PDE 59 (2020): Art. 122, 34 pp. pdf - ARTICLE available from springerlink.com pdf
Ph. LeFloch and A.E. Tzavaras, Existence theory for the Riemann problem for non-conservative hyperbolic systems, C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 347-352. pdf
Ph. LeFloch and A.E. Tzavaras, Representation of weak limits and definition of nonconservative products, SIAM J. Math. Anal. 30 (1999), 1309-1342. pdf - ARTICLE available at http://epubs.siam.org
Y.-J. Kim and A.E. Tzavaras, Diffusive N-waves and metastability in the Burgers equation, SIAM J. Math. Analysis 33 (2001), 607-633. pdf - ARTICLE available at http://epubs.siam.org
M. Slemrod and A.E. Tzavaras, A limiting viscosity approach for the Riemann problem in isentropic gas dynamics, Indiana Univ. Math. J. 38 (1989), 1047-1074. pdf - ARTICLE available at Journal site
A.E. Tzavaras, Elastic as limit of viscoelastic response, in a context of self-similar viscous limits, J. Differential Equations 123 (1995), 305-341. pdf
A.E. Tzavaras, Wave interactions and variation estimates for self-similar zero-viscosity limits in systems of conservation laws, Arch. Rational Mech. Anal. 135 (1996), 1-60. pdf - ARTICLE available at http://www.springerlink.com
Y.J. Kim and A.E. Tzavaras, 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. pdf
[ See also ]
J.A. Nohel, R.C. Rogers and A.E. Tzavaras, Weak solutions for a nonlinear system in viscoelasticity, Comm. Partial Differential Equations 13 (1988), 97-127. ARTICLE available at Journal Site
J.A. Nohel, R.C. Rogers and A.E. Tzavaras, Hyperbolic conservation laws in viscoelasticity, 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.
L. Gosse and A.E. Tzavaras, Convergence of relaxation schemes to the equations of elastodynamics, Math. Comp. 70 (2001), 555-577. pdf - ARTICLE available at http://www.ams.org
Ch. Arvanitis, Ch. Makridakis and A. Tzavaras, Stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws, SIAM J. Numer. Analysis 42 (2004), 1357-1393. pdf - ARTICLE available at http://epubs.siam.org
Multicomponent Convection Diffusion - Maxwell Stefan
Xiaokai Huo, Ansgar Juengel and A.E. Tzavaras, High-friction limits of Euler flows for multicomponent systems. Nonlinearity 32 (2019), 2875-2913. pdf - ARTICLE available from IOP Science
Xiaokai Huo, Hailiang Liu, A.E. Tzavaras and Shuaikun Wang. An energy stable and positivity preserving scheme for the Mazwell-Stefan diffusion system. SIAM J. Numerical Anal. 59 (5) (2021), 2321-2345. pdf - supplementary material - ARTICLE available from SIAM online
Xiaokai Huo, Ansgar Juengel and A.E. Tzavaras, Weak-Strong Uniquenes for Maxwell-Stefan systems. SIAM J. Math. Analysis 54 (3) (2022), 3215-3252. pdf - ARTICLE available from SIAM online
Stefanos Georgiadis and Athanasios E. Tzavaras, Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion. ESAIM: Math. Modeling Numer. Anal. 57 (1) (2023), 69-106. pdf - ARTICLE available from ESAIM
Xiaokai Huo, Ansgar Juengel and A.E. Tzavaras (2022). Existece and weak-strong uniqueness for Maxwell-Stefan Cahn-Hilliard systems. pdf
Stefanos Georgiadis, Ansgar Juengel and A.E. Tzavaras (2023). Nonisothermal multicomponent flows with mass diffusion and heat conduction. pdf
Y.-J. Kim and A.E. Tzavaras, Diffusive N-waves and metastability in the Burgers equation, SIAM J. Math. Analysis 33 (2001), 607-633. pdf - ARTICLE available at http://epubs.siam.org
C. Lattanzio and A.E. Tzavaras, Relative entropy in diffusive relaxation, SIAM J. Math. Analysis 45 (2013), 1563-1584. pdf - ARTICLE available at SIAM Journals online
A. Friedman and A.E. Tzavaras, A quasilinear parabolic system arising in modelling of catalytic reactors, J. Differential Equations 70 (1987), 167-196. ARTICLE available at Journal site
A. Friedman and A.E. Tzavaras, Combustion in a porous medium, SIAM J. Math. Anal. 19 (1988), 509-519. ARTICLE available at SIAM Journals online