Preprints and publications: Tzavaras

Preprints

Min-Gi Lee, Theodoros Katsaounis and Athanasios E. Tzavaras (2018)
Localization in adiabatic shear flow via geometric theory of singular perturbations.
J. Nonlinear Science (47 pp) (to appear)
pdf - ARTICLE available from springerlink.com

Publications by subject

Review Articles - Lecture Notes
Oscillations in Hyperbolic Problems - Kinetic Formulation
Kinetic Theory
Nonlinear Dynamics of Continuous Media
Hyperbolic Conservation Laws
Reaction-Convection-Diffusion Problems
- Convection Diffusion
- Reaction Diffusion

Review Articles - Lecture Notes

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
G.-Q. Chen and A.E. Tzavaras (2012)
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 (2014)
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

Oscillations in Hyperbolic Problems - Kinetic Formulation

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

Kinetic Theory

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
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.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
C. Lattanzio and A.E. Tzavaras (2013)
Relative entropy methods for hyperbolic and diffusive limits
Proceedings of the 14th International Conference on Hyperbolic Problems: Theory, Numerics and Applications (HYP2012) (to appear)
pdf
[ 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
F. Berthelin, A.E. Tzavaras and A. Vasseur (2009)
From discrete velocity Boltzmann equations to gas dynamics before shocks
J. Stat. Physics 135 (2009), 151-173.
pdf - ARTICLE available from springerlink.com

Polymers - Material Science

F. Otto and A. Tzavaras (2008)
Continuity of velocity gradients in suspensions of rod-like molecules
Comm. Math. Physics 277 (2008), 729-758.
ps - pdf - ARTICLE available at http://www.springerlink.com
D. Margetis and A.E. Tzavaras (2009)
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)

Nonlinear Dynamics of Continuous Media

Euler/Euler-Korteweg systems

C. Lattanzio and A.E. Tzavaras (2013)
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 (2015)
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 (2017)
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 (2016)
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 (2018)
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 (2019)
High-friction limits of Euler flows for multicomponent systems.
Nonlinearity 32 (2019), 2875-2913.
pdf - ARTICLE available from IOP Science

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. 1ational 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
A. Tzavaras (2005)
A relaxation theory with polyconvex entropy function converging to elastodynamics (unpublished)
ps - pdf
A. Tzavaras (2014)
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 (2012)
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 (2012)
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 (2014)
Convergence of variational approximation schemes for three dimensional elastodynamics with polyconvex energy
J. Anal. Appl. (ZAA) 33 (2014), 43-64.
pdf

Cavitation

J. Giesselmann and A.E. Tzavaras (2013)
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 (2014)
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 (2012)
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 (2014)
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

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
Th. Katsaounis and A.E. Tzavaras (2009)
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 (2010)
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 (2011)
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 (2014)
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 (2017)
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 (2017)
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 (2018)
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

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
Comm. Math. Physics 277 (2008), 729-758.
ps - pdf - ARTICLE available at http://www.springerlink.com

Hyperbolic Conservation Laws

Relative Entropy

C. Christoforou and A. Tzavaras (2017)
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 (2018)
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 (2018)
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 (2018)
Measure-valued solutions for the equations of adiabatic polyconvex thermoelasticity.
Discrete Cont. Dynam. Systems 39 (2019), 6175-6206.
pdf - ARTICLE available from AIMS Sciences

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

J.A. Nohel, R.C. Rogers and A.E. Tzavaras (1988)
Weak solutions for a nonlinear system in viscoelasticity
Comm. Partial Differential Equations 13 (1988), 97-127.
J.A. Nohel, R.C. Rogers and A.E. Tzavaras (1989)
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.