Knees, Dorothee; Thomas, Stephanie Optimal control of a rate-independent system constrained to parametrized balanced viscosity solutions. (English) Zbl 1512.49004 SIAM J. Control Optim. 61, No. 2, 723-754 (2023). MSC: 49J20 49J27 49J40 35D40 35Q74 74C05 PDFBibTeX XMLCite \textit{D. Knees} and \textit{S. Thomas}, SIAM J. Control Optim. 61, No. 2, 723--754 (2023; Zbl 1512.49004) Full Text: DOI arXiv
Herzog, Roland; Knees, Dorothee; Meyer, Christian; Sievers, Michael; Stötzner, Ailyn; Thomas, Stephanie Rate-independent systems and their viscous regularizations: analysis, simulation, and optimal control. (English) Zbl 1502.49016 Hintermüller, Michael (ed.) et al., Non-smooth and complementarity-based distributed parameter systems. Simulation and hierarchical optimization. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 172, 121-144 (2022). MSC: 49J52 49J27 49J40 74C05 74H15 PDFBibTeX XMLCite \textit{R. Herzog} et al., ISNM, Int. Ser. Numer. Math. 172, 121--144 (2022; Zbl 1502.49016) Full Text: DOI
Betz, Livia Vanishing-viscosity solutions to a rate-independent two-field gradient damage model. (English) Zbl 07813184 ZAMM, Z. Angew. Math. Mech. 101, No. 11, Article ID e201900226, 25 p. (2021). MSC: 74Rxx 74Axx 49Jxx PDFBibTeX XMLCite \textit{L. Betz}, ZAMM, Z. Angew. Math. Mech. 101, No. 11, Article ID e201900226, 25 p. (2021; Zbl 07813184) Full Text: DOI OA License
Kimura, Masato; Negri, Matteo Weak solutions for unidirectional gradient flows: existence, uniqueness, and convergence of time discretization schemes. (English) Zbl 1476.35127 NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 6, Paper No. 59, 46 p. (2021). MSC: 35K86 35K15 35R70 49J40 PDFBibTeX XMLCite \textit{M. Kimura} and \textit{M. Negri}, NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 6, Paper No. 59, 46 p. (2021; Zbl 1476.35127) Full Text: DOI
Knees, Dorothee; Shcherbakov, Viktor A penalized version of the local minimization scheme for rate-independent systems. (English) Zbl 1467.74039 Appl. Math. Lett. 115, Article ID 106954, 9 p. (2021). MSC: 74H80 49J21 PDFBibTeX XMLCite \textit{D. Knees} and \textit{V. Shcherbakov}, Appl. Math. Lett. 115, Article ID 106954, 9 p. (2021; Zbl 1467.74039) Full Text: DOI
Knees, Dorothee; Zanini, Chiara Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads. (English) Zbl 1458.35439 Discrete Contin. Dyn. Syst., Ser. S 14, No. 1, 121-149 (2021). MSC: 35R05 49J40 74C05 35Q74 35D40 49J45 PDFBibTeX XMLCite \textit{D. Knees} and \textit{C. Zanini}, Discrete Contin. Dyn. Syst., Ser. S 14, No. 1, 121--149 (2021; Zbl 1458.35439) Full Text: DOI arXiv
Krejcí, Pavel; Monteiro, Giselle A. What is the best viscous approximation to a rate-independent process? (English) Zbl 1446.49008 J. Convex Anal. 27, No. 3, 1015-1032 (2020). Reviewer: Hengyou Lan (Zigong) MSC: 49J40 47J20 90C31 47E05 PDFBibTeX XMLCite \textit{P. Krejcí} and \textit{G. A. Monteiro}, J. Convex Anal. 27, No. 3, 1015--1032 (2020; Zbl 1446.49008) Full Text: Link
Dondl, Patrick; Frenzel, Thomas; Mielke, Alexander A gradient system with a wiggly energy and relaxed EDP-convergence. (English) Zbl 1444.35101 ESAIM, Control Optim. Calc. Var. 25, Paper No. 68, 45 p. (2019). MSC: 35K55 35B27 35A15 49S05 49J40 49J45 PDFBibTeX XMLCite \textit{P. Dondl} et al., ESAIM, Control Optim. Calc. Var. 25, Paper No. 68, 45 p. (2019; Zbl 1444.35101) Full Text: DOI arXiv
Knees, Dorothee Convergence analysis of time-discretisation schemes for rate-independent systems. (English) Zbl 1437.49009 ESAIM, Control Optim. Calc. Var. 25, Paper No. 65, 38 p. (2019). MSC: 49J27 49J40 35Q74 65M12 74C05 74H15 PDFBibTeX XMLCite \textit{D. Knees}, ESAIM, Control Optim. Calc. Var. 25, Paper No. 65, 38 p. (2019; Zbl 1437.49009) Full Text: DOI arXiv
Meyer, Christian; Susu, Livia Mihaela Analysis of a viscous two-field gradient damage model. II: Penalization limit. (English) Zbl 1430.74128 Z. Anal. Anwend. 38, No. 4, 439-474 (2019). MSC: 74R05 35Q74 35R20 47J35 49J50 PDFBibTeX XMLCite \textit{C. Meyer} and \textit{L. M. Susu}, Z. Anal. Anwend. 38, No. 4, 439--474 (2019; Zbl 1430.74128) Full Text: DOI
Rossi, Riccarda Visco-energetic solutions to some rate-independent systems in damage, delamination, and plasticity. (English) Zbl 1425.35190 Math. Models Methods Appl. Sci. 29, No. 6, 1079-1138 (2019). MSC: 35Q74 49J40 74C05 74Rxx 74A45 74P10 PDFBibTeX XMLCite \textit{R. Rossi}, Math. Models Methods Appl. Sci. 29, No. 6, 1079--1138 (2019; Zbl 1425.35190) Full Text: DOI arXiv
Meyer, Christian; Susu, Livia Mihaela Analysis of a viscous two-field gradient damage model. I. Existence and uniqueness. (English) Zbl 1425.74407 Z. Anal. Anwend. 38, No. 3, 249-286 (2019). MSC: 74R05 35Q74 35R20 47J35 49J50 PDFBibTeX XMLCite \textit{C. Meyer} and \textit{L. M. Susu}, Z. Anal. Anwend. 38, No. 3, 249--286 (2019; Zbl 1425.74407) Full Text: DOI
Gilardi, Gianni; Sprekels, Jürgen Asymptotic limits and optimal control for the Cahn-Hilliard system with convection and dynamic boundary conditions. (English) Zbl 1404.35269 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 178, 1-31 (2019). Reviewer: Dian K. Palagachev (Bari) MSC: 35K61 35B40 49J20 49K20 93C20 PDFBibTeX XMLCite \textit{G. Gilardi} and \textit{J. Sprekels}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 178, 1--31 (2019; Zbl 1404.35269) Full Text: DOI arXiv
Francfort, Gilles A.; Mora, Maria Giovanna Quasistatic evolution in non-associative plasticity revisited. (English) Zbl 1387.74023 Calc. Var. Partial Differ. Equ. 57, No. 1, Paper No. 11, 22 p. (2018). MSC: 74C05 74L10 74G65 49J45 PDFBibTeX XMLCite \textit{G. A. Francfort} and \textit{M. G. Mora}, Calc. Var. Partial Differ. Equ. 57, No. 1, Paper No. 11, 22 p. (2018; Zbl 1387.74023) Full Text: DOI
Minotti, Luca; Savaré, Giuseppe Viscous corrections of the time incremental minimization scheme and visco-energetic solutions to rate-independent evolution problems. (English) Zbl 1387.74019 Arch. Ration. Mech. Anal. 227, No. 2, 477-543 (2018). MSC: 74B20 49J40 74R10 PDFBibTeX XMLCite \textit{L. Minotti} and \textit{G. Savaré}, Arch. Ration. Mech. Anal. 227, No. 2, 477--543 (2018; Zbl 1387.74019) Full Text: DOI arXiv
Mielke, Alexander (ed.); Peletier, Mark (ed.); Slepcev, Dejan (ed.) Variational methods for evolution. Abstracts from the workshop held November 12–18, 2017. (English) Zbl 1409.00100 Oberwolfach Rep. 14, No. 4, 3185-3261 (2017). MSC: 00B05 00B25 49-06 35-06 70-06 58E30 60F10 82C05 49Jxx PDFBibTeX XMLCite \textit{A. Mielke} (ed.) et al., Oberwolfach Rep. 14, No. 4, 3185--3261 (2017; Zbl 1409.00100) Full Text: DOI
Stefanelli, Ulisse; Wachsmuth, Daniel; Wachsmuth, Gerd Optimal control of a rate-independent evolution equation via viscous regularization. (English) Zbl 1369.49027 Discrete Contin. Dyn. Syst., Ser. S 10, No. 6, 1467-1485 (2017). MSC: 49K20 35K87 49J52 PDFBibTeX XMLCite \textit{U. Stefanelli} et al., Discrete Contin. Dyn. Syst., Ser. S 10, No. 6, 1467--1485 (2017; Zbl 1369.49027) Full Text: DOI arXiv
Crismale, Vito; Lazzaroni, Giuliano Quasistatic crack growth based on viscous approximation: a model with branching and kinking. (English) Zbl 1372.35376 NoDEA, Nonlinear Differ. Equ. Appl. 24, No. 1, Paper No. 7, 33 p. (2017). MSC: 35R35 35Q74 74R10 74G70 49J45 PDFBibTeX XMLCite \textit{V. Crismale} and \textit{G. Lazzaroni}, NoDEA, Nonlinear Differ. Equ. Appl. 24, No. 1, Paper No. 7, 33 p. (2017; Zbl 1372.35376) Full Text: DOI Link
Artina, Marco; Cagnetti, Filippo; Fornasier, Massimo; Solombrino, Francesco Linearly constrained evolutions of critical points and an application to cohesive fractures. (English) Zbl 1358.74053 Math. Models Methods Appl. Sci. 27, No. 2, 231-290 (2017). MSC: 74R99 49J27 74H10 74P10 74S20 PDFBibTeX XMLCite \textit{M. Artina} et al., Math. Models Methods Appl. Sci. 27, No. 2, 231--290 (2017; Zbl 1358.74053) Full Text: DOI arXiv
Minh, Mach Nguyet BV solutions constructed using the epsilon-neighborhood method. (English) Zbl 1338.49025 ESAIM, Control Optim. Calc. Var. 22, No. 1, 188-207 (2016). MSC: 49J45 49J20 49M30 49M25 PDFBibTeX XMLCite \textit{M. N. Minh}, ESAIM, Control Optim. Calc. Var. 22, No. 1, 188--207 (2016; Zbl 1338.49025) Full Text: DOI arXiv
Crismale, Vito; Lazzaroni, Giuliano Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model. (English) Zbl 1333.74021 Calc. Var. Partial Differ. Equ. 55, No. 1, Paper No. 17, 54 p. (2016). MSC: 74C05 74R05 74G65 35Q74 49J45 PDFBibTeX XMLCite \textit{V. Crismale} and \textit{G. Lazzaroni}, Calc. Var. Partial Differ. Equ. 55, No. 1, Paper No. 17, 54 p. (2016; Zbl 1333.74021) Full Text: DOI Link
Kraus, Christiane; Bonetti, Elena; Heinemann, Christian; Segatti, Antonio Modeling and analysis of a phase field system for damage and phase separation processes in solids. (English) Zbl 1333.35124 J. Differ. Equations 258, No. 11, 3928-3959 (2015). Reviewer: Ivan A. Parinov (Rostov-na-Donu) MSC: 35K85 35K55 49J40 49S05 35J50 74A45 74G25 34A12 82B26 82C26 35K92 PDFBibTeX XMLCite \textit{C. Kraus} et al., J. Differ. Equations 258, No. 11, 3928--3959 (2015; Zbl 1333.35124) Full Text: DOI arXiv
Roubíček, Tomáš Maximally-dissipative local solutions to rate-independent systems and application to damage and delamination problems. (English) Zbl 1304.35377 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 113, Part A, 33-50 (2015). MSC: 35K86 35M86 35Q74 49S05 65M12 74R20 74S30 35D30 PDFBibTeX XMLCite \textit{T. Roubíček}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 113, 33--50 (2015; Zbl 1304.35377) Full Text: DOI
Negri, M.; Zanini, C. From finite to linear elastic fracture mechanics by scaling. (English) Zbl 1297.49084 Calc. Var. Partial Differ. Equ. 50, No. 3-4, 525-548 (2014). Reviewer: Alain Brillard (Riedisheim) MSC: 49S05 49J45 74A45 PDFBibTeX XMLCite \textit{M. Negri} and \textit{C. Zanini}, Calc. Var. Partial Differ. Equ. 50, No. 3--4, 525--548 (2014; Zbl 1297.49084) Full Text: DOI Link
Cherfils, L.; Gatti, S.; Miranville, A. A variational approach to a Cahn-Hilliard model in a domain with nonpermeable walls. (English. Russian original) Zbl 1276.49014 J. Math. Sci., New York 189, No. 4, 604-636 (2013); translation from Probl. Mat. Anal. 69, 55-82 (2013). MSC: 49K40 49J40 35Q35 PDFBibTeX XMLCite \textit{L. Cherfils} et al., J. Math. Sci., New York 189, No. 4, 604--636 (2013; Zbl 1276.49014); translation from Probl. Mat. Anal. 69, 55--82 (2013) Full Text: DOI
Freddi, Lorenzo; Roubíček, Tomáš; Zanini, Chiara Quasistatic delamination of sandwich-like Kirchhoff-Love plates. (English) Zbl 1275.49019 J. Elasticity 113, No. 2, 219-250 (2013). MSC: 49J45 49S05 74K20 74R10 PDFBibTeX XMLCite \textit{L. Freddi} et al., J. Elasticity 113, No. 2, 219--250 (2013; Zbl 1275.49019) Full Text: DOI
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe Variational convergence of gradient flows and rate-independent evolutions in metric spaces. (English) Zbl 1255.49078 Milan J. Math. 80, No. 2, 381-410 (2012). MSC: 49Q20 34A60 PDFBibTeX XMLCite \textit{A. Mielke} et al., Milan J. Math. 80, No. 2, 381--410 (2012; Zbl 1255.49078) Full Text: DOI arXiv
Dal Maso, Gianni; DeSimone, Antonio; Solombrino, Francesco Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution. (English) Zbl 1311.74025 Calc. Var. Partial Differ. Equ. 44, No. 3-4, 495-541 (2012). MSC: 74C05 74L10 74G65 49L25 35K55 PDFBibTeX XMLCite \textit{G. Dal Maso} et al., Calc. Var. Partial Differ. Equ. 44, No. 3--4, 495--541 (2012; Zbl 1311.74025) Full Text: DOI
Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe BV solutions and viscosity approximations of rate-independent systems. (English) Zbl 1250.49041 ESAIM, Control Optim. Calc. Var. 18, No. 1, 36-80 (2012). Reviewer: Th. M. Rassias MSC: 49Q20 58E99 PDFBibTeX XMLCite \textit{A. Mielke} et al., ESAIM, Control Optim. Calc. Var. 18, No. 1, 36--80 (2012; Zbl 1250.49041) Full Text: DOI arXiv EuDML
Dal Maso, Gianni; DeSimone, Antonio; Solombrino, Francesco Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling. (English) Zbl 1311.74024 Calc. Var. Partial Differ. Equ. 40, No. 1-2, 125-181 (2011). MSC: 74C05 74L10 74G65 49J45 49L25 35K55 PDFBibTeX XMLCite \textit{G. Dal Maso} et al., Calc. Var. Partial Differ. Equ. 40, No. 1--2, 125--181 (2011; Zbl 1311.74024) Full Text: DOI
Knees, Dorothee; Zanini, Chiara; Mielke, Alexander Crack growth in polyconvex materials. (English) Zbl 1201.49013 Physica D 239, No. 15, 1470-1484 (2010). MSC: 49J52 49J40 49L25 35K90 74B20 74G65 74R10 PDFBibTeX XMLCite \textit{D. Knees} et al., Physica D 239, No. 15, 1470--1484 (2010; Zbl 1201.49013) Full Text: DOI
Yan, Xingjie; Wu, Ying; Zhong, Chengkui Uniform attractors for impulsive reaction-diffusion equations. (English) Zbl 1204.49036 Appl. Math. Comput. 216, No. 9, 2534-2543 (2010). MSC: 49N25 35K20 PDFBibTeX XMLCite \textit{X. Yan} et al., Appl. Math. Comput. 216, No. 9, 2534--2543 (2010; Zbl 1204.49036) Full Text: DOI
Roubíček, Tomáš Rate-independent processes in viscous solids at small strains. (English) Zbl 1239.35158 Math. Methods Appl. Sci. 32, No. 7, 825-862 (2009); erratum ibid. 32, No. 16, 2176 (2009). MSC: 35Q74 49S05 35K86 74C05 74F15 74N30 PDFBibTeX XMLCite \textit{T. Roubíček}, Math. Methods Appl. Sci. 32, No. 7, 825--862 (2009; Zbl 1239.35158) Full Text: DOI
Potra, Florian A. The Kantorovich theorem and interior point methods. (English) Zbl 1059.90137 Math. Program. 102, No. 1 (A), 47-70 (2005). MSC: 90C33 49M15 65H10 65K05 PDFBibTeX XMLCite \textit{F. A. Potra}, Math. Program. 102, No. 1 (A), 47--70 (2005; Zbl 1059.90137) Full Text: DOI
Mainik, Andreas; Mielke, Alexander Existence results for energetic models for rate-independent systems. (English) Zbl 1161.74387 Calc. Var. Partial Differ. Equ. 22, No. 1, 73-99 (2005). MSC: 74H20 49J10 74A45 74C15 74G65 74R10 PDFBibTeX XMLCite \textit{A. Mainik} and \textit{A. Mielke}, Calc. Var. Partial Differ. Equ. 22, No. 1, 73--99 (2005; Zbl 1161.74387) Full Text: DOI