Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

Publications

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Total result(s) found: 41
  • ​Th. Katsaounis, K. Kotsovos, I. Gereige, A. Al-Saggaf, A. Tzavaras, 2D simulation and performance evaluation of bifacial high efficiency c-Si solar cells under variable illumination conditions, (submitted)
Keywords:
bifacial solar cells, PERC device
  • ​M-G. Lee, A. Tzavaras, Localization in adiabatic shear flow via geometric theory of singular perturbations, (submitted)
Keywords:
adiabatic shear flow, geometric theory of singular perturbation
  • ​J. Giesselman, A. Tzavaras, Stability properties of the Euler-Korteweg system with nonmonotone pressures, Applicable Analysis, 96(9), 1528-1546, 2017
Keywords:
Euler–Kortweg system, phase transitions, Cahn–Hiliard equation
  • ​M-G. Lee, A. Tzavaras, Existence of localizing solutions in plasticity via geometric theory of singular perturbations,  SIAM J. Appl. Dyn. Syst, 16(1), 337-360, 2017
Keywords:
localization, shear bands, geometric singular perturbation theory
  • ​M-G Lee, Th. Katsaounis, A. Tzavaras, Localization of adiabatic deformations in thermoviscoplastic materials, to appear in proceeding of HYP2016
Keywords:
localization, Hadamard instability, shear bands
  • ​C. Christoforou, A. Tzavaras, On the relative entropy method for hyperbolic-parabolic systems, preprint
Keywords:
relative entropy, hyperbolic-parabolic system
  • Th. Katsaounis, M-G. Lee, A. Tzavaras, Localization in inelastic rate dependent shearing deformations​, Journal of Mechanics and Physics of Solids, 98(1):106-125, 2017
Keywords:
shear bands, Hadamard instability, shear localization
  • ​J. Giesselmann, C. Lattanzio, A.E. Tzavaras, Relative energy for the Korteweg-theory and related Hamiltonian flows in gas dynamic, Archive for Rational Mechanics and Analysis, 223(3), 1427-1484,2017
Keywords:
gas dynamics, Korteweg-theory
  • Th. Katsaounis, J. Olivier, A.E. Tzavaras, Emergence of coherent localized structures in shear deformations of temperature dependent fluids, Archive for Rational Mechanics and Analysis, 224(1), 173-208, 2017
Keywords:
Shear Band formation, Localized structures, Shear Deformation
  • Y-J. Kim, M-G. Lee, Existence and uniqueness in anisotropic conductivity reconstruction with Faraday’s law, (submitted)
Keywords:
Faraday’s law, anisotropic conductivity
Keywords:
soliton reflection, nonlinear Schrodinger
  • ​C. Christoforou, A.E. Tzavaras, Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity, 2016​
Keywords:
relative entropy, thermoviscoelasticity
  • ​M-G. Lee, M-S. Ko, Y-J. Kim, Orthotropic conductivity reconstruction with virtual resistive network and Faraday's law, Math. Methods Appl. Sciences, 39(5):1183-1196, 2016
Keywords:
conductivity image reconstruction, Faraday's law
  • ​A. Athanassoulis, Th. Katsaounis, I. Kyza, Regularized semiclassical limits: linear flows with infinite Lyapunov exponents, Communications in Math Sciences, 14(7):1821-1858, 2016
Keywords:
semiclassical limit for rough potential, Wigner transform, multivalued flow, selection principle, a posteriori error control
  • ​C. Lattanzio, A.E. Tzavaras, From gas dynamics with large friction to gradient flows describing diffusion theories, Communications in Partial Differential Equations, 42(2), 261-290, 2017
Keywords:
gradient flows, Wasserstein distance
  • ​Ch. Helzel, A.E. Tzavaras, A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows, Physica D: Nonlinear Phenomena, 337(1):18-29, 2016
Keywords:
macroscopic models rod-like particles
  • A. Athanassoulis, Th. Katsaounis, I. Kyza, On a selection principle for multivalued semiclassical flows​​
Keywords:
semiclassical limit for rough potential, smoothed Wigner transform, selection principle, a posteriori error control
  • ​Y-J. Kim, M-G. Lee, Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory, Quart. Appl. Math. 73 (2015), no.3, 419-433
Keywords:
conductivity image reconstruction
  • ​Ch. Helzel, A.E. Tzavaras, A kinetic model for the sedimentation of rod-like particles,  Multiscale Model. Simul., 15(1), 500-536, 2017
Keywords:
sedimentation, rod-like particles
  • ​A. Miroshnikov, A.E. Tzavaras, On the construction and properties of weak solutions describing dynamic cavitation, J. Elasticity 118 (2015), 141-185
Keywords:
Cavitation Shock wave Polyconvex elasticity
  • Y-J. Kim, M-G. Lee, M. Slemrod, Thermal Creep of a Rarefied Gas on the Basis of Non-linear Korteweg-Theory, Archive for Rational Mechanics and Analysis, 215(2): 353-379, 2015​​
Keywords:
Thermal Creep, Korteweg's Theory, Champan Enskog Expansion
  • ​Th. Katsaounis, I. Kyza, An adaptive finite element method for the linear Schrodinger equation, Numer. Math. 129(1):55-90, 2015​​​​​
Keywords:
Aposteriori Error Control, Adaptivity, Schrodinger eq., Finite Element Method
  • ​N. Christakis, Th. Katsaounis, G. Kossioris,  M. Plexousakis, On of the Performance of the WRF Numerical Model over Complex Terrain on a High Performance Computing Cluster, HPCC 2014, The 16th IEEE International Conference on High Performance Computing and Communications, Paris, France 2014
Keywords:
WRF model, performance evaluation
  • ​J. Giesselman, 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.
Keywords:
elastodynamics, cavitation
  • ​A. Miroshnikov, A.E. Tzavaras, Convergence of variational approximation schemes for three dimensional elastodynamims with polyconvex energy, J. Analysis Appl. (ZAA) 33 (2014), 43-64
Keywords:
Nonlinear elasticity, polyconvexity, variational approximation scheme
  • ​C. Lattanzio, A.E. Tzavaras, Relative entropy methods for hyperbolic and diffusive limits, 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
Keywords:
Hyperbolic Conservation Laws
  • ​A.E. Tzavaras, Stress relaxation models with polyconvex entropy in Lagrangian and Eulerian coordinates, Comm. in Information and Systems 13 (2013), 487-515
Keywords:
polyconvex elasticity, relaxation limits, pressure relaxation in gases
  • M-G. Lee, M-S. Ko,  Y-J. Kim, Virtual resistive network and conductivity reconstruction with Faradayʼs law, Inverse Problems, 30(12):125009,  2014
Keywords:
MREIT, virtual resistive network, mimetic discretization, isotropic conductivity
  • J. Giesselmann, A.E. Tzavaras, Singular limiting induced from continuum solutions and the problem of dynamic cavitation, Arch. Rational Mech. Anal. 212(1):​241-281​, 2014​​
Keywords:
Cavitation
  • ​J. Giesselmann, A. Miroshnikov, A.E. Tzavaras, The problem of dynamic cavitation in nonlinear elasticity, Seminaire Laurent Schwartz - EDP et applications (2012-2013), Exp No. 14, 17p.
Keywords:
nonlinear elasticity, cavitation
  • ​C. Lattanzio, A.E. Tzavaras, Relative entropy in diffusive relaxation, SIAM J. Math. Analysis 45 (2013), 1563-1584
Keywords:
relative entropy, diffusive relaxation, Euler equations
  • A. Miroshnikov, A.E. Tzavaras, Convergence of variational approximation schemes for three dimensional elastodynamims with polyconvex energy,  J. Analysis Appl. (ZAA)  33(1):43-64, 2013​​
Keywords:
Nonlinear elasticity, Polyconvexity, Variational approximation scheme
  • D. Dutykh, Th. Katsaounis, D. Mitsotakis, Finite volume methods for unidirectional dispersive wave model, Int. J. for Num. Methods in Fluids, 71(6): 717-736,  2013​​​​
Keywords:
finite volume method; nonlinear dispersive waves; unidirectional propagation; solitary waves; water waves
  • ​S. Demoulini, A.E. Tzavaras, D. Stuart, Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics, Arch. Rational Mech. Analysis 205 (2012), 927-961.
Keywords:
polyconvex elastodynamics
  • ​G-Q. Chen, A.E. Tzavaras, Remarks on the contributions of Constantine M. Dafermos to the subject of Conservation Laws, Acta Math. Scientia 32B (2012), 3-14
Keywords:
Hyperbolic Conservation Laws
  • ​A. Miroshnikov, A.E. Tzavaras, A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians, Comm. Math. Sciences 10 (2012), 87-115
Keywords:
elasticity, polyconvex, variational approximation
  • Th. Katsaounis, C. Simeoni, Three-points interfacial quadrature for geometrical source terms on nonuniform gridsCalcolo, 49(3):149-176, 2012
Keywords:
Geometrical source terms, Finite volume schemes, Nonuniform grids, Consistency, Optimal convergence rates
  • ​D. Dutykh, Th. Katsaounis,  D. Mitsotakis, Dispersive wave runup on non-uniform shores, Finite volumes for complex application VI,€“ Problems & Perspectives. Springer Proceedings in Mathematics, vol. 4, pp. 389 - 397, 2011
Keywords:
finite volume schemes, Boussinesq equation, runup
  • ​D. Dutykh, Th. Katsaounis, D. Mitsotakis, Finite volume schemes for Boussinesq type equations, Proceedings of Colloque EDP-Normandie, Caen, France, pp. 15-21, 2011
Keywords:
finite volume schemes, Boussinesq equation
  • ​Th. Katsaounis, 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
Keywords:
shear band, localization
  • D. Dutykh, Th. Katsaounis, D. Mitsotakis, Finite volume schemes for dispersive wave propagation and runupJournal of Computational Physics(JCP),  230(8):3035-3061, 2011​​​​
Keywords:
Finite volume method, Dispersive waves, Solitary waves, Runup, Water waves