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A convex-concave elliptic problem with a parameter on the boundary condition
Second order approximations of quasistatic evolution problems in finite dimension
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References:
[1] |
F. Cagnetti, A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path,, Math. Models Methods Appl. Sci., 18 (2008), 1027.
doi: 10.1142/S0218202508002942. |
[2] |
G. Dal Maso, A. DeSimone, M. G. Mora and M. Morini, A vanishing viscosity approach to quasistatic evolution in plasticity with softening,, Arch. Ration. Mech. Anal., 189 (2008), 469.
doi: 10.1007/s00205-008-0117-5. |
[3] |
G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling,, Calc. Var. Partial Differential Equations, 40 (2011), 125. Google Scholar |
[4] |
G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution,, SISSA preprint 46/2010/M., (). Google Scholar |
[5] |
G. Dal Maso and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case,, Netw. Heterog. Media, 5 (2010), 97.
|
[6] |
M. A. Efendiev and A. Mielke, On the rate-independent limit of systems with dry friction and small viscosity,, J. Convex Anal., 13 (2006), 151.
|
[7] |
J. Guckenheimer and P. Holme, "Nonlinear Oscillations, Dynamical Systems, and Bifurcations on Vector Fields,", Applied Mathematical Sciences, 42 (1983).
|
[8] |
J. K. Hale, "Ordinary Differential Equations,", Pure and Applied Mathematics, XX1 (1980). Google Scholar |
[9] |
M. W. Hirsch, "Differential Topology,", Graduate Texts in Mathematics, 33 (1976). Google Scholar |
[10] |
D. Knees, A. Mielke and C. Zanini, Crack growth in polyconvex materials,, Phys. D, 239 (2010), 1470.
doi: 10.1016/j.physd.2009.02.008. |
[11] |
A. Mielke, R. Rossi and G. Savaré, Modeling solutions with jumps for rate-independent systems on metric spaces,, Discrete Contin. Dyn. Syst., 25 (2009), 585.
doi: 10.3934/dcds.2009.25.585. |
[12] |
A. Mielke, R. Rossi and G. Savaré, BV solutions and viscosity approximations of rate-independent systems,, ESAIM Control Optim. Calc. Var., (2011).
doi: 10.1051/cocv/2010054. |
[13] |
F. Solombrino, Quasistatic evolution for plasticity with softening: the spatially homogeneous case,, Discrete Contin. Dyn. Syst., 27 (2010), 1189.
doi: 10.3934/dcds.2010.27.1189. |
[14] |
R. Toader and C. Zanini, An artificial viscosity approach to quasistatic crack growth,, Boll. Unione Mat. Ital. (9), 2 (2009), 1.
|
[15] |
C. Zanini, Singular perturbation of finite dimensional gradient flows,, Discrete Contin. Dyn. Syst., 18 (2007), 657.
doi: 10.3934/dcds.2007.18.657. |
show all references
References:
[1] |
F. Cagnetti, A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path,, Math. Models Methods Appl. Sci., 18 (2008), 1027.
doi: 10.1142/S0218202508002942. |
[2] |
G. Dal Maso, A. DeSimone, M. G. Mora and M. Morini, A vanishing viscosity approach to quasistatic evolution in plasticity with softening,, Arch. Ration. Mech. Anal., 189 (2008), 469.
doi: 10.1007/s00205-008-0117-5. |
[3] |
G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling,, Calc. Var. Partial Differential Equations, 40 (2011), 125. Google Scholar |
[4] |
G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution,, SISSA preprint 46/2010/M., (). Google Scholar |
[5] |
G. Dal Maso and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case,, Netw. Heterog. Media, 5 (2010), 97.
|
[6] |
M. A. Efendiev and A. Mielke, On the rate-independent limit of systems with dry friction and small viscosity,, J. Convex Anal., 13 (2006), 151.
|
[7] |
J. Guckenheimer and P. Holme, "Nonlinear Oscillations, Dynamical Systems, and Bifurcations on Vector Fields,", Applied Mathematical Sciences, 42 (1983).
|
[8] |
J. K. Hale, "Ordinary Differential Equations,", Pure and Applied Mathematics, XX1 (1980). Google Scholar |
[9] |
M. W. Hirsch, "Differential Topology,", Graduate Texts in Mathematics, 33 (1976). Google Scholar |
[10] |
D. Knees, A. Mielke and C. Zanini, Crack growth in polyconvex materials,, Phys. D, 239 (2010), 1470.
doi: 10.1016/j.physd.2009.02.008. |
[11] |
A. Mielke, R. Rossi and G. Savaré, Modeling solutions with jumps for rate-independent systems on metric spaces,, Discrete Contin. Dyn. Syst., 25 (2009), 585.
doi: 10.3934/dcds.2009.25.585. |
[12] |
A. Mielke, R. Rossi and G. Savaré, BV solutions and viscosity approximations of rate-independent systems,, ESAIM Control Optim. Calc. Var., (2011).
doi: 10.1051/cocv/2010054. |
[13] |
F. Solombrino, Quasistatic evolution for plasticity with softening: the spatially homogeneous case,, Discrete Contin. Dyn. Syst., 27 (2010), 1189.
doi: 10.3934/dcds.2010.27.1189. |
[14] |
R. Toader and C. Zanini, An artificial viscosity approach to quasistatic crack growth,, Boll. Unione Mat. Ital. (9), 2 (2009), 1.
|
[15] |
C. Zanini, Singular perturbation of finite dimensional gradient flows,, Discrete Contin. Dyn. Syst., 18 (2007), 657.
doi: 10.3934/dcds.2007.18.657. |
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