-
Previous Article
On a p-curl system arising in electromagnetism
- DCDS-S Home
- This Issue
-
Next Article
A family of nonlinear diffusions connecting Perona-Malik to standard diffusion
Rate-independent processes with linear growth energies and time-dependent boundary conditions
1. | Institute of Information Theory and Automation of the ASCR, Pod vodárenskou věží 4, CZ-182 08 Praha 8, Czech Republic |
2. | Department of Mathematical Sciences, University of Bath, Bath BA2 7AY |
References:
[1] |
I. V. Chenchiah, M. O. Rieger and J. Zimmer, Gradient flows in asymmetric metric spaces, Nonlinear Anal., 71 (2009), 5820-5834.
doi: 10.1016/j.na.2009.05.006. |
[2] |
S. Conti and M. Ortiz, Dislocation microstructures and the effective behavior of single crystals, Arch. Ration. Mech. Anal., 176 (2005), 103-147.
doi: 10.1007/s00205-004-0353-2. |
[3] |
G. Dal Maso, G. A. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity, Arch. Ration. Mech. Anal., 176 (2005), 165-225.
doi: 10.1007/s00205-004-0351-4. |
[4] |
R. J. DiPerna and A. J. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys., 108 (1987), 667-689.
doi: 10.1007/BF01214424. |
[5] |
G. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies, J. Reine Angew. Math., 595 (2006), 55-91.
doi: 10.1515/CRELLE.2006.044. |
[6] |
M. Kružík and T. Roubíček, On the measures of DiPerna and Majda, Math. Bohem., 122 (1997), 383-399. |
[7] |
M. Kružík and J. Zimmer, A model of shape memory alloys accounting for plasticity, IMA Journal of Applied Mathematics, 76 (2011), 193-216.
doi: 10.1093/imamat/hxq058. |
[8] |
M. Kružík and J. Zimmer, Vanishing regularisation for gradient flows via $\Gamma$-limit,, in preparation., ().
|
[9] |
M. Kružík and J. Zimmer, Evolutionary problems in non-reflexive spaces, ESAIM Control Optim. Calc. Var., 16 (2010), 1-22. |
[10] |
A. Mainik and A. Mielke, Global existence for rate-independent gradient plasticity at finite strain, J. Nonlinear Sci., 19 (2009), 221-248.
doi: 10.1007/s00332-008-9033-y. |
[11] |
A. Mielke and T. Roubíček, A rate-independent model for inelastic behavior of shape-memory alloys, Multiscale Model. Simul., 1 (2003), 571-597 (electronic).
doi: 10.1137/S1540345903422860. |
[12] |
A. Mielke, F. Theil and V. I. Levitas, A variational formulation of rate-independent phase transformations using an extremum principle, Arch. Ration. Mech. Anal., 162 (2002), 137-177.
doi: 10.1007/s002050200194. |
[13] |
M. Ortiz and E. A. Repetto, Nonconvex energy minimization and dislocation structures in ductile single crystals, J. Mech. Phys. Solids, 47 (1999), 397-462.
doi: 10.1016/S0022-5096(97)00096-3. |
[14] |
T. Roubíček, "Relaxation in Optimization Theory and Variational Calculus,'' de Gruyter Series in Nonlinear Analysis and Applications, 4, Walter de Gruyter & Co., Berlin, 1997. |
[15] |
J. Souček, Spaces of functions on domain $\Omega $, whose $k$-th derivatives are measures defined on $\bar \Omega $, Časopis Pĕst. Mat., 97 (1972), 10-46, 94. |
[16] |
D. W. Stroock and S. R. S. Varadhan, "Multidimensional Diffusion Processes,'' Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 233, Springer-Verlag, Berlin-New York, 1979. |
show all references
References:
[1] |
I. V. Chenchiah, M. O. Rieger and J. Zimmer, Gradient flows in asymmetric metric spaces, Nonlinear Anal., 71 (2009), 5820-5834.
doi: 10.1016/j.na.2009.05.006. |
[2] |
S. Conti and M. Ortiz, Dislocation microstructures and the effective behavior of single crystals, Arch. Ration. Mech. Anal., 176 (2005), 103-147.
doi: 10.1007/s00205-004-0353-2. |
[3] |
G. Dal Maso, G. A. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity, Arch. Ration. Mech. Anal., 176 (2005), 165-225.
doi: 10.1007/s00205-004-0351-4. |
[4] |
R. J. DiPerna and A. J. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys., 108 (1987), 667-689.
doi: 10.1007/BF01214424. |
[5] |
G. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies, J. Reine Angew. Math., 595 (2006), 55-91.
doi: 10.1515/CRELLE.2006.044. |
[6] |
M. Kružík and T. Roubíček, On the measures of DiPerna and Majda, Math. Bohem., 122 (1997), 383-399. |
[7] |
M. Kružík and J. Zimmer, A model of shape memory alloys accounting for plasticity, IMA Journal of Applied Mathematics, 76 (2011), 193-216.
doi: 10.1093/imamat/hxq058. |
[8] |
M. Kružík and J. Zimmer, Vanishing regularisation for gradient flows via $\Gamma$-limit,, in preparation., ().
|
[9] |
M. Kružík and J. Zimmer, Evolutionary problems in non-reflexive spaces, ESAIM Control Optim. Calc. Var., 16 (2010), 1-22. |
[10] |
A. Mainik and A. Mielke, Global existence for rate-independent gradient plasticity at finite strain, J. Nonlinear Sci., 19 (2009), 221-248.
doi: 10.1007/s00332-008-9033-y. |
[11] |
A. Mielke and T. Roubíček, A rate-independent model for inelastic behavior of shape-memory alloys, Multiscale Model. Simul., 1 (2003), 571-597 (electronic).
doi: 10.1137/S1540345903422860. |
[12] |
A. Mielke, F. Theil and V. I. Levitas, A variational formulation of rate-independent phase transformations using an extremum principle, Arch. Ration. Mech. Anal., 162 (2002), 137-177.
doi: 10.1007/s002050200194. |
[13] |
M. Ortiz and E. A. Repetto, Nonconvex energy minimization and dislocation structures in ductile single crystals, J. Mech. Phys. Solids, 47 (1999), 397-462.
doi: 10.1016/S0022-5096(97)00096-3. |
[14] |
T. Roubíček, "Relaxation in Optimization Theory and Variational Calculus,'' de Gruyter Series in Nonlinear Analysis and Applications, 4, Walter de Gruyter & Co., Berlin, 1997. |
[15] |
J. Souček, Spaces of functions on domain $\Omega $, whose $k$-th derivatives are measures defined on $\bar \Omega $, Časopis Pĕst. Mat., 97 (1972), 10-46, 94. |
[16] |
D. W. Stroock and S. R. S. Varadhan, "Multidimensional Diffusion Processes,'' Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 233, Springer-Verlag, Berlin-New York, 1979. |
[1] |
Riccarda Rossi, Ulisse Stefanelli, Marita Thomas. Rate-independent evolution of sets. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 89-119. doi: 10.3934/dcdss.2020304 |
[2] |
Ulisse Stefanelli, Daniel Wachsmuth, Gerd Wachsmuth. Optimal control of a rate-independent evolution equation via viscous regularization. Discrete and Continuous Dynamical Systems - S, 2017, 10 (6) : 1467-1485. doi: 10.3934/dcdss.2017076 |
[3] |
Martin Heida, Alexander Mielke. Averaging of time-periodic dissipation potentials in rate-independent processes. Discrete and Continuous Dynamical Systems - S, 2017, 10 (6) : 1303-1327. doi: 10.3934/dcdss.2017070 |
[4] |
Gianni Dal Maso, Alexander Mielke, Ulisse Stefanelli. Preface: Rate-independent evolutions. Discrete and Continuous Dynamical Systems - S, 2013, 6 (1) : i-ii. doi: 10.3934/dcdss.2013.6.1i |
[5] |
T. J. Sullivan, M. Koslowski, F. Theil, Michael Ortiz. Thermalization of rate-independent processes by entropic regularization. Discrete and Continuous Dynamical Systems - S, 2013, 6 (1) : 215-233. doi: 10.3934/dcdss.2013.6.215 |
[6] |
Augusto Visintin. Structural stability of rate-independent nonpotential flows. Discrete and Continuous Dynamical Systems - S, 2013, 6 (1) : 257-275. doi: 10.3934/dcdss.2013.6.257 |
[7] |
Boumedièene Chentouf, Sabeur Mansouri. Boundary stabilization of a flexible structure with dynamic boundary conditions via one time-dependent delayed boundary control. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 1127-1141. doi: 10.3934/dcdss.2021090 |
[8] |
Nicola Guglielmi, László Hatvani. On small oscillations of mechanical systems with time-dependent kinetic and potential energy. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 911-926. doi: 10.3934/dcds.2008.20.911 |
[9] |
Alexander Zlotnik, Ilya Zlotnik. Finite element method with discrete transparent boundary conditions for the time-dependent 1D Schrödinger equation. Kinetic and Related Models, 2012, 5 (3) : 639-667. doi: 10.3934/krm.2012.5.639 |
[10] |
Daniele Davino, Ciro Visone. Rate-independent memory in magneto-elastic materials. Discrete and Continuous Dynamical Systems - S, 2015, 8 (4) : 649-691. doi: 10.3934/dcdss.2015.8.649 |
[11] |
Alexander Mielke, Riccarda Rossi, Giuseppe Savaré. Modeling solutions with jumps for rate-independent systems on metric spaces. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 585-615. doi: 10.3934/dcds.2009.25.585 |
[12] |
Michela Eleuteri, Luca Lussardi, Ulisse Stefanelli. A rate-independent model for permanent inelastic effects in shape memory materials. Networks and Heterogeneous Media, 2011, 6 (1) : 145-165. doi: 10.3934/nhm.2011.6.145 |
[13] |
Stefano Bosia, Michela Eleuteri, Elisabetta Rocca, Enrico Valdinoci. Preface: Special issue on rate-independent evolutions and hysteresis modelling. Discrete and Continuous Dynamical Systems - S, 2015, 8 (4) : i-i. doi: 10.3934/dcdss.2015.8.4i |
[14] |
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu. Periodic solutions for time-dependent subdifferential evolution inclusions. Evolution Equations and Control Theory, 2017, 6 (2) : 277-297. doi: 10.3934/eect.2017015 |
[15] |
Eduard Marušić-Paloka, Igor Pažanin. Reaction of the fluid flow on time-dependent boundary perturbation. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1227-1246. doi: 10.3934/cpaa.2019059 |
[16] |
Hedy Attouch, Alexandre Cabot, Zaki Chbani, Hassan Riahi. Rate of convergence of inertial gradient dynamics with time-dependent viscous damping coefficient. Evolution Equations and Control Theory, 2018, 7 (3) : 353-371. doi: 10.3934/eect.2018018 |
[17] |
Luca Minotti. Visco-Energetic solutions to one-dimensional rate-independent problems. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5883-5912. doi: 10.3934/dcds.2017256 |
[18] |
Dorothee Knees, Chiara Zanini. Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 121-149. doi: 10.3934/dcdss.2020332 |
[19] |
Alice Fiaschi. Rate-independent phase transitions in elastic materials: A Young-measure approach. Networks and Heterogeneous Media, 2010, 5 (2) : 257-298. doi: 10.3934/nhm.2010.5.257 |
[20] |
Michela Eleuteri, Luca Lussardi. Thermal control of a rate-independent model for permanent inelastic effects in shape memory materials. Evolution Equations and Control Theory, 2014, 3 (3) : 411-427. doi: 10.3934/eect.2014.3.411 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]