Knees, Dorothee; Zanini, Chiara Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads. (English) Zbl 07314552 Discrete Contin. Dyn. Syst., Ser. S 14, No. 1, 121-149 (2021). MSC: 35R05 49J40 74C05 35Q74 35D40 49J45 PDF BibTeX XML Cite \textit{D. Knees} and \textit{C. Zanini}, Discrete Contin. Dyn. Syst., Ser. S 14, No. 1, 121--149 (2021; Zbl 07314552) Full Text: DOI
Kolpakova, E. A. Approximation of a multivalued solution of the Hamilton-Jacobi equation. (English. Russian original) Zbl 1448.35104 Math. Notes 108, No. 1, 77-86 (2020); translation from Mat. Zametki 108, No. 1, 81-93 (2020). MSC: 35F21 35D40 49J35 49L25 PDF BibTeX XML Cite \textit{E. A. Kolpakova}, Math. Notes 108, No. 1, 77--86 (2020; Zbl 1448.35104); translation from Mat. Zametki 108, No. 1, 81--93 (2020) Full Text: DOI
Kühn, Franziska Existence of (Markovian) solutions to martingale problems associated with Lévy-type operators. (English) Zbl 1448.60162 Electron. J. Probab. 25, Paper No. 16, 26 p. (2020). Reviewer: Ze-Chun Hu (Chengdu) MSC: 60J35 60J25 60H10 60J76 45K05 35S05 60G51 PDF BibTeX XML Cite \textit{F. Kühn}, Electron. J. Probab. 25, Paper No. 16, 26 p. (2020; Zbl 1448.60162) Full Text: DOI Euclid
Ke, Guoyi; Guo, Wei An alternative formulation of discontinous Galerkin schemes for solving Hamilton-Jacobi equations. (English) Zbl 1417.65173 J. Sci. Comput. 78, No. 2, 1023-1044 (2019). MSC: 65M60 65M06 35D40 35F21 35L65 PDF BibTeX XML Cite \textit{G. Ke} and \textit{W. Guo}, J. Sci. Comput. 78, No. 2, 1023--1044 (2019; Zbl 1417.65173) Full Text: DOI
Bian, Baojun; Chen, Xinfu; Xu, Zuo Quan Utility maximization under trading constraints with discontinuous utility. (English) Zbl 1411.91482 SIAM J. Financ. Math. 10, No. 1, 243-260 (2019). MSC: 91G10 91B16 49L25 93E20 PDF BibTeX XML Cite \textit{B. Bian} et al., SIAM J. Financ. Math. 10, No. 1, 243--260 (2019; Zbl 1411.91482) Full Text: DOI
Chen, Xiaohong; Li, Zhilin; Ruiz Álvarez, Juan A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids. (English) Zbl 1410.76281 Comput. Fluids 172, 549-563 (2018). MSC: 76M20 65N06 35Q35 35R05 65N22 76D07 PDF BibTeX XML Cite \textit{X. Chen} et al., Comput. Fluids 172, 549--563 (2018; Zbl 1410.76281) Full Text: DOI
El Hajj, Ahmad; Ibrahim, Hassan; Rizik, Vivian Global \(BV\) solution for a non-local coupled system modeling the dynamics of dislocation densities. (English) Zbl 1378.35265 J. Differ. Equations 264, No. 3, 1750-1785 (2018). MSC: 35Q53 49L25 35F25 35L40 35L45 65M06 65M12 65M15 74H20 74H25 35F21 35Q74 74B20 PDF BibTeX XML Cite \textit{A. El Hajj} et al., J. Differ. Equations 264, No. 3, 1750--1785 (2018; Zbl 1378.35265) Full Text: DOI
Minbashian, Hadi; Adibi, Hojatolah; Dehghan, Mehdi An adaptive wavelet space-time SUPG method for hyperbolic conservation laws. (English) Zbl 1383.65126 Numer. Methods Partial Differ. Equations 33, No. 6, 2062-2089 (2017). MSC: 65M60 35L65 65T60 35L67 65M12 35L05 76B15 PDF BibTeX XML Cite \textit{H. Minbashian} et al., Numer. Methods Partial Differ. Equations 33, No. 6, 2062--2089 (2017; Zbl 1383.65126) Full Text: DOI
Karlsen, K. H.; Towers, J. D. Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition. (English) Zbl 1380.65158 J. Hyperbolic Differ. Equ. 14, No. 4, 671-701 (2017). MSC: 65M06 35L65 PDF BibTeX XML Cite \textit{K. H. Karlsen} and \textit{J. D. Towers}, J. Hyperbolic Differ. Equ. 14, No. 4, 671--701 (2017; Zbl 1380.65158) Full Text: DOI
Neilan, Michael; Salgado, Abner J.; Zhang, Wujun Numerical analysis of strongly nonlinear PDEs. (English) Zbl 1381.65092 Acta Numerica 26, 137-303 (2017). Reviewer: Rolf Dieter Grigorieff (Berlin) MSC: 65N30 65N06 65N12 65N15 65N22 35J57 35J66 60H15 35J96 35F21 PDF BibTeX XML Cite \textit{M. Neilan} et al., Acta Numerica 26, 137--303 (2017; Zbl 1381.65092) Full Text: DOI arXiv
Gassner, Gregor; Staudenmaier, Marc; Hindenlang, Florian; Atak, Muhammed; Munz, Claus-Dieter A space-time adaptive discontinuous Galerkin scheme. (English) Zbl 1390.65106 Comput. Fluids 117, 247-261 (2015). MSC: 65M60 65M50 PDF BibTeX XML Cite \textit{G. Gassner} et al., Comput. Fluids 117, 247--261 (2015; Zbl 1390.65106) Full Text: DOI
Boudjerada, R.; El Hajj, A. Global existence results for eikonal equation with \(BV\) initial data. (English) Zbl 1327.35066 NoDEA, Nonlinear Differ. Equ. Appl. 22, No. 4, 947-978 (2015). MSC: 35F25 35A01 74G25 35F21 70H20 35Q74 PDF BibTeX XML Cite \textit{R. Boudjerada} and \textit{A. El Hajj}, NoDEA, Nonlinear Differ. Equ. Appl. 22, No. 4, 947--978 (2015; Zbl 1327.35066) Full Text: DOI
Kawohl, Bernd; Schuricht, Friedemann First eigenfunctions of the 1-Laplacian are viscosity solutions. (English) Zbl 1322.35106 Commun. Pure Appl. Anal. 14, No. 1, 329-339 (2015). Reviewer: Nikos Katzourakis (Reading) MSC: 35P30 35D40 PDF BibTeX XML Cite \textit{B. Kawohl} and \textit{F. Schuricht}, Commun. Pure Appl. Anal. 14, No. 1, 329--339 (2015; Zbl 1322.35106) Full Text: DOI Link
Takei, R.; Chen, W.; Clawson, Z.; Kirov, S.; Vladimirsky, A. Optimal control with budget constraints and resets. (English) Zbl 1322.90091 SIAM J. Control Optim. 53, No. 2, 712-744 (2015). MSC: 90C29 49L20 49L25 49N90 65N22 65K05 34A38 PDF BibTeX XML Cite \textit{R. Takei} et al., SIAM J. Control Optim. 53, No. 2, 712--744 (2015; Zbl 1322.90091) Full Text: DOI
Liu, Hailiang The alternating evolution methods for first order nonlinear partial differential equations. (English) Zbl 1308.65168 Commun. Inf. Syst. 13, No. 3, 291-325 (2013). MSC: 65M60 65M06 65M08 35L05 35F21 49L25 PDF BibTeX XML Cite \textit{H. Liu}, Commun. Inf. Syst. 13, No. 3, 291--325 (2013; Zbl 1308.65168) Full Text: DOI
Rao, Zhiping; Zidani, Hasnaa Hamilton-Jacobi-Bellman equations on multi-domains. (English) Zbl 1272.49046 Bredies, Kristian (ed.) et al., Control and optimization with PDE constraints. Based on the international workshop on control and optimization of PDEs, Mariatrost, Austria, October 10–14, 2011. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0630-5/hbk; 978-3-0348-0631-2/ebook). ISNM. International Series of Numerical Mathematics 164, 93-116 (2013). MSC: 49L25 49L20 35F21 PDF BibTeX XML Cite \textit{Z. Rao} and \textit{H. Zidani}, ISNM, Int. Ser. Numer. Math. 164, 93--116 (2013; Zbl 1272.49046) Full Text: DOI
Giga, Yoshikazu; Hamamuki, Nao Hamilton-Jacobi equations with discontinuous source terms. (English) Zbl 1263.35066 Commun. Partial Differ. Equations 38, No. 1-3, 199-243 (2013). MSC: 35F21 35F25 49L25 35D40 PDF BibTeX XML Cite \textit{Y. Giga} and \textit{N. Hamamuki}, Commun. Partial Differ. Equations 38, No. 1--3, 199--243 (2013; Zbl 1263.35066) Full Text: DOI
Cockburn, Bernardo; Merev, Ivan; Qian, Jianliang Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. (English) Zbl 1269.65086 Math. Comput. 82, No. 281, 187-212 (2013). Reviewer: Fernando Casas (Castellon) MSC: 65M15 65M12 35F21 49L25 65M06 65M08 65M60 PDF BibTeX XML Cite \textit{B. Cockburn} et al., Math. Comput. 82, No. 281, 187--212 (2013; Zbl 1269.65086) Full Text: DOI
Jimenez, Julien Mathematical analysis of a scalar multidimensional conservation law with discontinuous flux. (English) Zbl 1232.35094 J. Evol. Equ. 11, No. 3, 553-576 (2011). MSC: 35L65 35L04 35R05 PDF BibTeX XML Cite \textit{J. Jimenez}, J. Evol. Equ. 11, No. 3, 553--576 (2011; Zbl 1232.35094) Full Text: DOI
Guo, Wei; Li, Fengyan; Qiu, Jianxian Local-structure-preserving discontinuous Galerkin methods with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations. (English) Zbl 1217.65193 J. Sci. Comput. 47, No. 2, 239-257 (2011). MSC: 65M60 35F21 65M06 49L25 65Y20 PDF BibTeX XML Cite \textit{W. Guo} et al., J. Sci. Comput. 47, No. 2, 239--257 (2011; Zbl 1217.65193) Full Text: DOI
Goreac, Dan; Serea, Oana-Silvia Mayer and optimal stopping stochastic control problems with discontinuous cost. (English) Zbl 1215.93150 J. Math. Anal. Appl. 380, No. 1, 327-342 (2011). MSC: 93E20 49L25 49J40 60H10 49N15 PDF BibTeX XML Cite \textit{D. Goreac} and \textit{O.-S. Serea}, J. Math. Anal. Appl. 380, No. 1, 327--342 (2011; Zbl 1215.93150) Full Text: DOI
Yan, Jue; Osher, Stanley A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations. (English) Zbl 1205.65271 J. Comput. Phys. 230, No. 1, 232-244 (2011). MSC: 65M60 35F21 65M12 65M15 49L25 PDF BibTeX XML Cite \textit{J. Yan} and \textit{S. Osher}, J. Comput. Phys. 230, No. 1, 232--244 (2011; Zbl 1205.65271) Full Text: DOI
Kumar, Ajeet; Vladimirsky, Alexander An efficient method for multiobjective optimal control and optimal control subject to integral constraints. (English) Zbl 1240.90345 J. Comput. Math. 28, No. 4, 517-551 (2010). MSC: 90C29 49J30 49L25 65K05 PDF BibTeX XML Cite \textit{A. Kumar} and \textit{A. Vladimirsky}, J. Comput. Math. 28, No. 4, 517--551 (2010; Zbl 1240.90345) Full Text: DOI arXiv
Chambolle, Antonin; Novaga, Matteo Implicit time discretization of the mean curvature flow with a discontinuous forcing term. (English) Zbl 1170.65054 Interfaces Free Bound. 10, No. 3, 283-300 (2008). Reviewer: Ronald H. W. Hoppe (Augsburg) MSC: 65K10 49Q05 49L25 PDF BibTeX XML Cite \textit{A. Chambolle} and \textit{M. Novaga}, Interfaces Free Bound. 10, No. 3, 283--300 (2008; Zbl 1170.65054) Full Text: DOI Link
Abgrall, Rémi; Perrier, Vincent On the numerical approximation of first-order Hamilton-Jacobi equations. (English) Zbl 1147.65323 Int. J. Appl. Math. Comput. Sci. 17, No. 3, 403-412 (2007). MSC: 65N30 35L60 35F15 65N06 65M06 49L25 PDF BibTeX XML Cite \textit{R. Abgrall} and \textit{V. Perrier}, Int. J. Appl. Math. Comput. Sci. 17, No. 3, 403--412 (2007; Zbl 1147.65323) Full Text: DOI EuDML
Bressan, Alberto; Hong, Yunho Optimal control problems on stratified domains. (English) Zbl 1123.49028 Netw. Heterog. Media 2, No. 2, 313-331 (2007). Reviewer: Lars Grüne (Bayreuth) MSC: 49L25 49J24 PDF BibTeX XML Cite \textit{A. Bressan} and \textit{Y. Hong}, Netw. Heterog. Media 2, No. 2, 313--331 (2007; Zbl 1123.49028) Full Text: DOI
Guo, Yuzhen; Feng, Enmin A nonlinear model and viscosity solution for the temperature field of an oil-immersed self-cooled three-phrase transformer. (English) Zbl 1112.35088 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66, No. 9, 2098-2107 (2007). MSC: 35K50 35K55 35R05 35D05 PDF BibTeX XML Cite \textit{Y. Guo} and \textit{E. Feng}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66, No. 9, 2098--2107 (2007; Zbl 1112.35088) Full Text: DOI
Tsai, Yen-Hsi Richard; Giga, Yoshikazu; Osher, Stanley A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations. (English) Zbl 1013.65088 Math. Comput. 72, No. 241, 159-181 (2003). MSC: 65M06 70H20 35L60 49L25 PDF BibTeX XML Cite \textit{Y.-H. R. Tsai} et al., Math. Comput. 72, No. 241, 159--181 (2003; Zbl 1013.65088) Full Text: DOI
Plaskacz, Sławomir; Quincampoix, Marc On representation formulas for Hamilton Jacobi’s equations related to calculus of variations problems. (English) Zbl 1021.49024 Topol. Methods Nonlinear Anal. 20, No. 1, 85-118 (2002). Reviewer: Ştefan Mirică (Bucureşti) MSC: 49L25 34A60 35D05 49J52 49J24 49L20 PDF BibTeX XML Cite \textit{S. Plaskacz} and \textit{M. Quincampoix}, Topol. Methods Nonlinear Anal. 20, No. 1, 85--118 (2002; Zbl 1021.49024) Full Text: DOI
Barles, G.; Busca, Jérôme Existence and comparison results for fully nonlinear degenerate elliptic equations without Zeroth-order term. (English) Zbl 0997.35023 Commun. Partial Differ. Equations 26, No. 11-12, 2323-2337 (2001). MSC: 35J70 35J60 35B05 35D05 PDF BibTeX XML Cite \textit{G. Barles} and \textit{J. Busca}, Commun. Partial Differ. Equations 26, No. 11--12, 2323--2337 (2001; Zbl 0997.35023) Full Text: DOI
Augoula, Steeve; Abgrall, Rémi A discontinuous projection algorithm for Hamilton Jacobi equations. (English) Zbl 0945.65111 Cockburn, Bernardo (ed.) et al., Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24-26, 1999. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 11, 255-261 (2000). MSC: 65M60 35L60 PDF BibTeX XML Cite \textit{S. Augoula} and \textit{R. Abgrall}, Lect. Notes Comput. Sci. Eng. 11, 255--261 (2000; Zbl 0945.65111)
Lepsky, Olga; Hu, Changqing; Shu, Chi-Wang Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations. (English) Zbl 0968.65073 Appl. Numer. Math. 33, No. 1-4, 423-434 (2000). Reviewer: Vladimir Gorbunov (Ul’yanovsk) MSC: 65M60 35L60 65M12 65Y20 PDF BibTeX XML Cite \textit{O. Lepsky} et al., Appl. Numer. Math. 33, No. 1--4, 423--434 (2000; Zbl 0968.65073) Full Text: DOI
Motta, M.; Rampazzo, F. State constrained control problems with neither coercivity nor \(L^1\) bounds on the controls. (English) Zbl 0969.49012 Ann. Mat. Pura Appl., IV. Ser. 177, 117-142 (1999). Reviewer: Ştefan Mirică (Bucureşti) MSC: 49L20 49L25 93C10 49N25 PDF BibTeX XML Cite \textit{M. Motta} and \textit{F. Rampazzo}, Ann. Mat. Pura Appl. (4) 177, 117--142 (1999; Zbl 0969.49012) Full Text: DOI
Ostapenko, V. V. On the strong monotonicity of nonlinear difference schemes. (English. Russian original) Zbl 0964.65084 Comput. Math. Math. Phys. 38, No. 7, 1119-1133 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 7, 1170-1185 (1998). Reviewer: Alexey Tret’yakov (Siedlce) MSC: 65M06 65M12 PDF BibTeX XML Cite \textit{V. V. Ostapenko}, Comput. Math. Math. Phys. 38, No. 7, 1119--1133 (1998; Zbl 0964.65084); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 7, 1170--1185 (1998)
Herzog, Matthias Error estimates for approximative methods as applied to Majda’s model of dynamic combustion. (Fehlerabschätzungen für approximative Verfahren angewandt auf Majdas Modell der dynamischen Verbrennung.) (German) Zbl 0913.65080 Bonner Mathematische Schriften. 310. Bonn: Universität Bonn, Mathematisch-Naturwissenschaftliche Fakultät, 101 p. (1998). MSC: 65M15 80A25 76L05 35L60 35Q72 80A32 PDF BibTeX XML Cite \textit{M. Herzog}, Fehlerabschätzungen für approximative Verfahren angewandt auf Majdas Modell der dynamischen Verbrennung. Bonn: Universität Bonn, Mathematisch-Naturwissenschaftliche Fakultät (1998; Zbl 0913.65080)
Camilli, Fabio; Siconolfi, Antonio Discontinuous solutions of a Hamilton-Jacobi equation with infinite speed of propagation. (English) Zbl 0888.35024 SIAM J. Math. Anal. 28, No. 6, 1420-1445 (1997). MSC: 35F25 49L25 PDF BibTeX XML Cite \textit{F. Camilli} and \textit{A. Siconolfi}, SIAM J. Math. Anal. 28, No. 6, 1420--1445 (1997; Zbl 0888.35024) Full Text: DOI
Subbotin, A. I. Discontinuous solutions of a Dirichlet-type boundary-value problem for the first-order partial differential equation. (English) Zbl 0821.35027 Russ. J. Numer. Anal. Math. Model. 8, No. 2, 145-164 (1993). MSC: 35F30 35D05 PDF BibTeX XML Cite \textit{A. I. Subbotin}, Russ. J. Numer. Anal. Math. Model. 8, No. 2, 145--164 (1993; Zbl 0821.35027) Full Text: DOI
Tadmor, Eitan Local error estimates for discontinuous solutions of nonlinear hyperbolic equations. (English) Zbl 0732.65084 SIAM J. Numer. Anal. 28, No. 4, 891-906 (1991). Reviewer: U. Göhner (Stuttgart) MSC: 65M06 65M15 35L65 PDF BibTeX XML Cite \textit{E. Tadmor}, SIAM J. Numer. Anal. 28, No. 4, 891--906 (1991; Zbl 0732.65084) Full Text: DOI
Bertsch, Michiel; Dal Passo, Roberta; Ughi, Maura Discontinuous “viscosity” solutions of a degenerate parabolic equation. (English) Zbl 0714.35039 Trans. Am. Math. Soc. 320, No. 2, 779-798 (1990). Reviewer: W.Walter MSC: 35K65 35D10 35K60 PDF BibTeX XML Cite \textit{M. Bertsch} et al., Trans. Am. Math. Soc. 320, No. 2, 779--798 (1990; Zbl 0714.35039) Full Text: DOI
Lavery, John E. Nonoscillatory solution of the steady-state inviscid Burgers’ equation by mathematical programming. (English) Zbl 0665.65068 J. Comput. Phys. 79, No. 2, 436-448 (1988). Reviewer: H.F.Bauer MSC: 65L10 34B30 76M45 76D10 PDF BibTeX XML Cite \textit{J. E. Lavery}, J. Comput. Phys. 79, No. 2, 436--448 (1988; Zbl 0665.65068) Full Text: DOI
Barles, G.; Perthame, B. Discontinuous solutions of deterministic optimal stopping time problems. (English) Zbl 0629.49017 RAIRO, Modélisation Math. Anal. Numér. 21, 557-579 (1987). Reviewer: E.Barron MSC: 49L20 35F20 49J40 60G40 35D05 49J45 PDF BibTeX XML Cite \textit{G. Barles} and \textit{B. Perthame}, RAIRO, Modélisation Math. Anal. Numér. 21, 557--579 (1987; Zbl 0629.49017) Full Text: DOI EuDML
Hooper, Alison; Duffy, B. R.; Moffatt, H. K. Flow of fluid of non-uniform viscosity in converging and diverging channels. (English) Zbl 0492.76111 J. Fluid Mech. 117, 283-304 (1982). MSC: 76V05 76D05 PDF BibTeX XML Cite \textit{A. Hooper} et al., J. Fluid Mech. 117, 283--304 (1982; Zbl 0492.76111) Full Text: DOI