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Invariant regions and global existence for a phase field model
Clamped elastic-ideally plastic beams and Prandtl-Ishlinskii hysteresis operators
1. | Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin |
[1] |
Wei Liu, Pavel Krejčí, Guoju Ye. Continuity properties of Prandtl-Ishlinskii operators in the space of regulated functions. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3783-3795. doi: 10.3934/dcdsb.2017190 |
[2] |
Pavel Krejčí, Harbir Lamba, Sergey Melnik, Dmitrii Rachinskii. Kurzweil integral representation of interacting Prandtl-Ishlinskii operators. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 2949-2965. doi: 10.3934/dcdsb.2015.20.2949 |
[3] |
Dmitrii Rachinskii. On geometric conditions for reduction of the Moreau sweeping process to the Prandtl-Ishlinskii operator. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3361-3386. doi: 10.3934/dcdsb.2018246 |
[4] |
Thomas Hillen, Kevin J. Painter, Amanda C. Swan, Albert D. Murtha. Moments of von mises and fisher distributions and applications. Mathematical Biosciences & Engineering, 2017, 14 (3) : 673-694. doi: 10.3934/mbe.2017038 |
[5] |
Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479 |
[6] |
Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic and Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707 |
[7] |
Antonio DeSimone, Natalie Grunewald, Felix Otto. A new model for contact angle hysteresis. Networks and Heterogeneous Media, 2007, 2 (2) : 211-225. doi: 10.3934/nhm.2007.2.211 |
[8] |
Shigeru Takata, Masanari Hattori, Takumu Miyauchi. On the entropic property of the Ellipsoidal Statistical model with the prandtl number below 2/3. Kinetic and Related Models, 2020, 13 (6) : 1163-1174. doi: 10.3934/krm.2020041 |
[9] |
Vincenzo Recupero. Hysteresis operators in metric spaces. Discrete and Continuous Dynamical Systems - S, 2015, 8 (4) : 773-792. doi: 10.3934/dcdss.2015.8.773 |
[10] |
Faker Ben Belgacem. Uniqueness for an ill-posed reaction-dispersion model. Application to organic pollution in stream-waters. Inverse Problems and Imaging, 2012, 6 (2) : 163-181. doi: 10.3934/ipi.2012.6.163 |
[11] |
Peter Benner, Tobias Breiten, Carsten Hartmann, Burkhard Schmidt. Model reduction of controlled Fokker–Planck and Liouville–von Neumann equations. Journal of Computational Dynamics, 2020, 7 (1) : 1-33. doi: 10.3934/jcd.2020001 |
[12] |
Martin Brokate, Pavel Krejčí. Weak differentiability of scalar hysteresis operators. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2405-2421. doi: 10.3934/dcds.2015.35.2405 |
[13] |
Pavel Krejčí. The Preisach hysteresis model: Error bounds for numerical identification and inversion. Discrete and Continuous Dynamical Systems - S, 2013, 6 (1) : 101-119. doi: 10.3934/dcdss.2013.6.101 |
[14] |
Youssef Amal, Martin Campos Pinto. Global solutions for an age-dependent model of nucleation, growth and ageing with hysteresis. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 517-535. doi: 10.3934/dcdsb.2010.13.517 |
[15] |
Joachim Naumann, Jörg Wolf. On Prandtl's turbulence model: Existence of weak solutions to the equations of stationary turbulent pipe-flow. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1371-1390. doi: 10.3934/dcdss.2013.6.1371 |
[16] |
Shigeru Takata, Masanari Hattori, Takumu Miyauchi. Erratum to: On the entropic property of the ellipsoidal statistical model with the Prandtl number below 2/3. Kinetic and Related Models, , () : -. doi: 10.3934/krm.2022013 |
[17] |
Marcio A. Jorge Silva, Vando Narciso, André Vicente. On a beam model related to flight structures with nonlocal energy damping. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3281-3298. doi: 10.3934/dcdsb.2018320 |
[18] |
Michela Eleuteri, Jana Kopfová, Pavel Krejčí. A new phase field model for material fatigue in an oscillating elastoplastic beam. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2465-2495. doi: 10.3934/dcds.2015.35.2465 |
[19] |
Yue Sun, Zhijian Yang. Strong attractors and their robustness for an extensible beam model with energy damping. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3101-3129. doi: 10.3934/dcdsb.2021175 |
[20] |
Antonio DeSimone, Martin Kružík. Domain patterns and hysteresis in phase-transforming solids: Analysis and numerical simulations of a sharp interface dissipative model via phase-field approximation. Networks and Heterogeneous Media, 2013, 8 (2) : 481-499. doi: 10.3934/nhm.2013.8.481 |
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