Bürger, Raimund; Careaga, Julio; Diehl, Stefan; Pineda, Romel A moving-boundary model of reactive settling in wastewater treatment. II: numerical scheme. (English) Zbl 07635765 Appl. Math. Modelling 111, 247-269 (2022). MSC: 35K65 35Q35 65M06 76V05 PDF BibTeX XML Cite \textit{R. Bürger} et al., Appl. Math. Modelling 111, 247--269 (2022; Zbl 07635765) Full Text: DOI OpenURL
Wei, Qianqian; Wang, Guodong; Ma, Yanying High-order Godunov-type scheme for conservation laws with discontinuous flux function in space. (English) Zbl 07539546 Int. J. Comput. Methods 19, No. 3, Article ID 2150066, 20 p. (2022). MSC: 65-XX 76-XX PDF BibTeX XML Cite \textit{Q. Wei} et al., Int. J. Comput. Methods 19, No. 3, Article ID 2150066, 20 p. (2022; Zbl 07539546) Full Text: DOI OpenURL
Badwaik, Jayesh; Klingenberg, Christian; Risebro, Nils Henrik; Ruf, Adrian M. Multilevel Monte Carlo finite volume methods for random conservation laws with discontinuous flux. (English) Zbl 07405591 ESAIM, Math. Model. Numer. Anal. 55, No. 3, 1039-1065 (2021). MSC: 65-XX 35L65 35R05 65C05 65M12 PDF BibTeX XML Cite \textit{J. Badwaik} et al., ESAIM, Math. Model. Numer. Anal. 55, No. 3, 1039--1065 (2021; Zbl 07405591) Full Text: DOI arXiv OpenURL
Bürger, Raimund; Chalons, Christophe; Ordoñez, Rafael; Villada, Luis Miguel A multiclass Lighthill-Whitham-Richards traffic model with a discontinuous velocity function. (English) Zbl 1473.65095 Netw. Heterog. Media 16, No. 2, 187-219 (2021). MSC: 65M06 35L45 35L65 76A99 PDF BibTeX XML Cite \textit{R. Bürger} et al., Netw. Heterog. Media 16, No. 2, 187--219 (2021; Zbl 1473.65095) Full Text: DOI OpenURL
Hu, Yanbo; Wang, Guodong The resonance behavior for the coupling of two Aw-Rascle traffic models. (English) Zbl 1487.35054 Adv. Difference Equ. 2020, Paper No. 60, 23 p. (2020). MSC: 35B34 35R35 PDF BibTeX XML Cite \textit{Y. Hu} and \textit{G. Wang}, Adv. Difference Equ. 2020, Paper No. 60, 23 p. (2020; Zbl 1487.35054) Full Text: DOI OpenURL
Ancona, Fabio; Chiri, Maria Teresa Attainable profiles for conservation laws with flux function spatially discontinuous at a single point. (English) Zbl 1458.35263 ESAIM, Control Optim. Calc. Var. 26, Paper No. 124, 33 p. (2020). MSC: 35L65 35F25 93B05 PDF BibTeX XML Cite \textit{F. Ancona} and \textit{M. T. Chiri}, ESAIM, Control Optim. Calc. Var. 26, Paper No. 124, 33 p. (2020; Zbl 1458.35263) Full Text: DOI arXiv OpenURL
Cheng, Hongjun; Yang, Hanchun Riemann problem for the 2D scalar conservation law involving linear fluxes with discontinuous coefficients. (English) Zbl 1454.35248 J. Math. Phys. 61, No. 11, 111504, 20 p. (2020). MSC: 35Q15 35C06 35L67 76L05 35R05 PDF BibTeX XML Cite \textit{H. Cheng} and \textit{H. Yang}, J. Math. Phys. 61, No. 11, 111504, 20 p. (2020; Zbl 1454.35248) Full Text: DOI OpenURL
Goatin, Paola; Rossi, Elena Comparative study of macroscopic traffic flow models at road junctions. (English) Zbl 1452.35098 Netw. Heterog. Media 15, No. 2, 261-279 (2020). Reviewer: Giuseppe Maria Coclite (Bari) MSC: 35L65 90B20 82B21 65M08 PDF BibTeX XML Cite \textit{P. Goatin} and \textit{E. Rossi}, Netw. Heterog. Media 15, No. 2, 261--279 (2020; Zbl 1452.35098) Full Text: DOI OpenURL
Andreianov, Boris; Rosini, Massimiliano D. Microscopic selection of solutions to scalar conservation laws with discontinuous flux in the context of vehicular traffic. (English) Zbl 1494.35114 Banasiak, Jacek (ed.) et al., Semigroups of operators – theory and applications. Selected papers based on the presentations at the conference, SOTA 2018, Kazimierz Dolny, Poland, September 30 – October 5, 2018. In honour of Jan Kisyński’s 85th birthday. Cham: Springer. Springer Proc. Math. Stat. 325, 113-135 (2020). MSC: 35L65 90B20 35A35 PDF BibTeX XML Cite \textit{B. Andreianov} and \textit{M. D. Rosini}, Springer Proc. Math. Stat. 325, 113--135 (2020; Zbl 1494.35114) Full Text: DOI HAL OpenURL
Sun, Xia; Wang, Guodong; Ma, Yanying A new modified local Lax-Friedrichs scheme for scalar conservation laws with discontinuous flux. (English) Zbl 1436.65111 Appl. Math. Lett. 105, Article ID 106328, 7 p. (2020). MSC: 65M06 35Q35 PDF BibTeX XML Cite \textit{X. Sun} et al., Appl. Math. Lett. 105, Article ID 106328, 7 p. (2020; Zbl 1436.65111) Full Text: DOI OpenURL
Badwaik, Jayesh; Ruf, Adrian M. Convergence rates of monotone schemes for conservation laws with discontinuous flux. (English) Zbl 1440.65107 SIAM J. Numer. Anal. 58, No. 1, 607-629 (2020). MSC: 65M08 65M12 35R05 35L65 35L45 PDF BibTeX XML Cite \textit{J. Badwaik} and \textit{A. M. Ruf}, SIAM J. Numer. Anal. 58, No. 1, 607--629 (2020; Zbl 1440.65107) Full Text: DOI arXiv OpenURL
Risebro, Nils Henrik Three models for two phase flow in porous media. (English) Zbl 1430.76447 Vietnam J. Math. 47, No. 4, 835-849 (2019). MSC: 76S05 65M06 76M20 35L65 35Q35 76T99 PDF BibTeX XML Cite \textit{N. H. Risebro}, Vietnam J. Math. 47, No. 4, 835--849 (2019; Zbl 1430.76447) Full Text: DOI Link OpenURL
Rosini, Massimiliano Systems of conservation laws with discontinuous fluxes and applications to traffic. (English) Zbl 1430.35236 Ann. Univ. Mariae Curie-Skłodowska, Sect. A 73, No. 2, 135-173 (2019). MSC: 35R05 35L65 35L45 90B20 34A34 PDF BibTeX XML Cite \textit{M. Rosini}, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 73, No. 2, 135--173 (2019; Zbl 1430.35236) Full Text: DOI OpenURL
Guerra, Graziano; Shen, Wen Vanishing viscosity and backward Euler approximations for conservation laws with discontinuous flux. (English) Zbl 1428.35211 SIAM J. Math. Anal. 51, No. 4, 3112-3144 (2019). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 35L65 35R05 35L60 PDF BibTeX XML Cite \textit{G. Guerra} and \textit{W. Shen}, SIAM J. Math. Anal. 51, No. 4, 3112--3144 (2019; Zbl 1428.35211) Full Text: DOI OpenURL
Dine, Houssein Nasser El; Saad, Mazen; Talhouk, Raafat Existence results for a monophasic compressible Darcy-Brinkman’s flow in porous media. (English) Zbl 1426.35187 J. Elliptic Parabol. Equ. 5, No. 1, 125-147 (2019). MSC: 35Q35 35A01 35A02 35D30 76S05 35G25 35G40 PDF BibTeX XML Cite \textit{H. N. E. Dine} et al., J. Elliptic Parabol. Equ. 5, No. 1, 125--147 (2019; Zbl 1426.35187) Full Text: DOI OpenURL
Ghaderi Zefreh, Masoud; Nilsen, Halvor M.; Lie, Knut Andreas; Raynaud, Xavier; Doster, Florian Streamline simulation of a reactive advective flow with discontinuous flux function. (English) Zbl 1414.76056 Comput. Geosci. 23, No. 2, 255-271 (2019). MSC: 76S05 35L45 35L60 35L65 76V05 PDF BibTeX XML Cite \textit{M. Ghaderi Zefreh} et al., Comput. Geosci. 23, No. 2, 255--271 (2019; Zbl 1414.76056) Full Text: DOI OpenURL
Bressan, Alberto; Guerra, Graziano; Shen, Wen Vanishing viscosity solutions for conservation laws with regulated flux. (English) Zbl 1421.35212 J. Differ. Equations 266, No. 1, 312-351 (2019). Reviewer: Jörg Härterich (Bochum) MSC: 35L65 35R05 35K15 35F21 35B25 PDF BibTeX XML Cite \textit{A. Bressan} et al., J. Differ. Equations 266, No. 1, 312--351 (2019; Zbl 1421.35212) Full Text: DOI arXiv OpenURL
Shen, Wen Global Riemann solvers for several \(3\times3\) systems of conservation laws with degeneracies. (English) Zbl 1416.35164 Math. Models Methods Appl. Sci. 28, No. 8, 1599-1626 (2018). Reviewer: Vishnu Dutt Sharma (Mumbai) MSC: 35L67 35L65 35L80 35L60 35L45 PDF BibTeX XML Cite \textit{W. Shen}, Math. Models Methods Appl. Sci. 28, No. 8, 1599--1626 (2018; Zbl 1416.35164) Full Text: DOI arXiv OpenURL
Bürger, Raimund; Diehl, Stefan; Mejías, Camilo A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation. (English) Zbl 1412.65068 ESAIM, Math. Model. Numer. Anal. 52, No. 2, 365-392 (2018). Reviewer: Kai Schneider (Marseille) MSC: 65M06 35K57 65M12 PDF BibTeX XML Cite \textit{R. Bürger} et al., ESAIM, Math. Model. Numer. Anal. 52, No. 2, 365--392 (2018; Zbl 1412.65068) Full Text: DOI OpenURL
Towers, John D. Convergence via OSLC of the Godunov scheme for a scalar conservation law with time and space flux discontinuities. (English) Zbl 1395.65042 Numer. Math. 139, No. 4, 939-969 (2018). MSC: 65M08 65M12 35L65 PDF BibTeX XML Cite \textit{J. D. Towers}, Numer. Math. 139, No. 4, 939--969 (2018; Zbl 1395.65042) Full Text: DOI OpenURL
Towers, John D. Convergence of the Godunov scheme for a scalar conservation law with time and space discontinuities. (English) Zbl 1406.35190 J. Hyperbolic Differ. Equ. 15, No. 2, 175-190 (2018). MSC: 35L65 65M06 65M08 65M12 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Hyperbolic Differ. Equ. 15, No. 2, 175--190 (2018; Zbl 1406.35190) Full Text: DOI OpenURL
Wang, Guodong; Hu, Yanbo The Roe-type interface flux for conservation laws with discontinuous flux function. (English) Zbl 1377.65112 Appl. Math. Lett. 75, 68-73 (2018). MSC: 65M06 35L65 PDF BibTeX XML Cite \textit{G. Wang} and \textit{Y. Hu}, Appl. Math. Lett. 75, 68--73 (2018; Zbl 1377.65112) Full Text: DOI OpenURL
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 OpenURL
Benkhaldoun, Fayssal; Halassi, A.; Ouazar, Driss; Seaid, Mohammed; Taik, Ahmed Slope limiters for radial basis functions applied to conservation laws with discontinuous flux function. (English) Zbl 1403.76137 Eng. Anal. Bound. Elem. 66, 49-65 (2016). MSC: 76M22 65M70 35L45 35L65 76A99 PDF BibTeX XML Cite \textit{F. Benkhaldoun} et al., Eng. Anal. Bound. Elem. 66, 49--65 (2016; Zbl 1403.76137) Full Text: DOI OpenURL
Adimurthi, A.; Aggarwal, Aekta; Veerappa Gowda, G. D. Godunov-type numerical methods for a model of granular flow. (English) Zbl 1349.76297 J. Comput. Phys. 305, 1083-1118 (2016). MSC: 76M12 76M20 65M08 65M06 76T25 PDF BibTeX XML Cite \textit{A. Adimurthi} et al., J. Comput. Phys. 305, 1083--1118 (2016; Zbl 1349.76297) Full Text: DOI OpenURL
Khorsandi, Saeid; Shen, Wen; Johns, Russell T. Global Riemann solver and front tracking approximation of three-component gas floods. (English) Zbl 1353.35202 Q. Appl. Math. 74, No. 4, 607-632 (2016). Reviewer: Qin Meng Zhao (Beijing) MSC: 35L65 35F55 35Q35 35A35 35L67 PDF BibTeX XML Cite \textit{S. Khorsandi} et al., Q. Appl. Math. 74, No. 4, 607--632 (2016; Zbl 1353.35202) Full Text: DOI OpenURL
Adimurthi; Kumar Kenettinkara, Sudarshan; Veerappa Gowda, G. D. On the convergence of a second order approximation of conservation laws with discontinuous flux. (English) Zbl 1339.65146 Bull. Braz. Math. Soc. (N.S.) 47, No. 1, 21-35 (2016). MSC: 65M12 35L65 65M06 PDF BibTeX XML Cite \textit{Adimurthi} et al., Bull. Braz. Math. Soc. (N.S.) 47, No. 1, 21--35 (2016; Zbl 1339.65146) Full Text: DOI OpenURL
Shen, Wen On the Cauchy problems for polymer flooding with gravitation. (English) Zbl 1382.35162 J. Differ. Equations 261, No. 1, 627-653 (2016). MSC: 35L65 35A01 35L45 76S05 PDF BibTeX XML Cite \textit{W. Shen}, J. Differ. Equations 261, No. 1, 627--653 (2016; Zbl 1382.35162) Full Text: DOI OpenURL
Ghoshal, Shyam Sundar BV regularity near the interface for nonuniform convex discontinuous flux. (English) Zbl 1343.35050 Netw. Heterog. Media 11, No. 2, 331-348 (2016). MSC: 35B65 35L65 35L67 35F21 PDF BibTeX XML Cite \textit{S. S. Ghoshal}, Netw. Heterog. Media 11, No. 2, 331--348 (2016; Zbl 1343.35050) Full Text: DOI arXiv OpenURL
Andreianov, Boris; Cancès, Clément On interface transmission conditions for conservation laws with discontinuous flux of general shape. (English) Zbl 1336.35230 J. Hyperbolic Differ. Equ. 12, No. 2, 343-384 (2015). Reviewer: Evgeniy Panov (Novgorod) MSC: 35L65 35R05 65M08 PDF BibTeX XML Cite \textit{B. Andreianov} and \textit{C. Cancès}, J. Hyperbolic Differ. Equ. 12, No. 2, 343--384 (2015; Zbl 1336.35230) Full Text: DOI OpenURL
Shen, Wen Slow erosion with rough geological layers. (English) Zbl 1329.35199 SIAM J. Math. Anal. 47, No. 4, 3116-3150 (2015). MSC: 35L65 35L67 35L03 45K05 35R09 PDF BibTeX XML Cite \textit{W. Shen}, SIAM J. Math. Anal. 47, No. 4, 3116--3150 (2015; Zbl 1329.35199) Full Text: DOI OpenURL
Shen, Chun; Sun, Meina Instability of Riemann solutions to a scalar conservation law with discontinuous flux. (English) Zbl 1320.35212 Z. Angew. Math. Phys. 66, No. 3, 499-515 (2015). MSC: 35L65 35L67 35B30 76N10 35A35 PDF BibTeX XML Cite \textit{C. Shen} and \textit{M. Sun}, Z. Angew. Math. Phys. 66, No. 3, 499--515 (2015; Zbl 1320.35212) Full Text: DOI OpenURL
Ghoshal, Shyam Sundar Optimal results on TV bounds for scalar conservation laws with discontinuous flux. (English) Zbl 1312.35032 J. Differ. Equations 258, No. 3, 980-1014 (2015). MSC: 35B45 35L65 35F21 PDF BibTeX XML Cite \textit{S. S. Ghoshal}, J. Differ. Equations 258, No. 3, 980--1014 (2015; Zbl 1312.35032) Full Text: DOI OpenURL
Coclite, G. M.; Mishra, S.; Risebro, N. H.; Weber, F. Analysis and numerical approximation of Brinkman regularization of two-phase flows in porous media. (English) Zbl 1392.76075 Comput. Geosci. 18, No. 5, 637-659 (2014). MSC: 76S05 65M06 35Q86 PDF BibTeX XML Cite \textit{G. M. Coclite} et al., Comput. Geosci. 18, No. 5, 637--659 (2014; Zbl 1392.76075) Full Text: DOI OpenURL
Sudarshan Kumar, K.; Praveen, C.; Veerappa Gowda, G. D. A finite volume method for a two-phase multicomponent polymer flooding. (English) Zbl 1349.76829 J. Comput. Phys. 275, 667-695 (2014). MSC: 76S05 76M12 65M08 76T30 PDF BibTeX XML Cite \textit{K. Sudarshan Kumar} et al., J. Comput. Phys. 275, 667--695 (2014; Zbl 1349.76829) Full Text: DOI OpenURL
Andreianov, Boris; Brenner, Konstantin; Cancès, Clément Approximating the vanishing capillarity limit of two-phase flow in multi-dimensional heterogeneous porous medium. (English) Zbl 1297.76152 ZAMM, Z. Angew. Math. Mech. 94, No. 7-8, 655-667 (2014). MSC: 76S05 76M12 76M10 76Txx PDF BibTeX XML Cite \textit{B. Andreianov} et al., ZAMM, Z. Angew. Math. Mech. 94, No. 7--8, 655--667 (2014; Zbl 1297.76152) Full Text: DOI HAL OpenURL
Adimurthi; Kumar K, Sudarshan; Veerappa Gowda, G. D. Second order scheme for scalar conservation laws with discontinuous flux. (English) Zbl 1329.65177 Appl. Numer. Math. 80, 46-64 (2014). MSC: 65M06 65M12 PDF BibTeX XML Cite \textit{Adimurthi} et al., Appl. Numer. Math. 80, 46--64 (2014; Zbl 1329.65177) Full Text: DOI arXiv OpenURL
Andreianov, Boris; Cancès, Clément Vanishing capillarity solutions of Buckley-Leverett equation with gravity in two-rocks’ medium. (English) Zbl 1392.76033 Comput. Geosci. 17, No. 3, 551-572 (2013). MSC: 76M12 35L02 35L65 65M08 76S05 PDF BibTeX XML Cite \textit{B. Andreianov} and \textit{C. Cancès}, Comput. Geosci. 17, No. 3, 551--572 (2013; Zbl 1392.76033) Full Text: DOI OpenURL
Shen, Chun; Sun, Meina Wave interactions and stability of the Riemann solutions for a scalar conservation law with a discontinuous flux function. (English) Zbl 1272.35151 Z. Angew. Math. Phys. 64, No. 4, 1025-1056 (2013). MSC: 35L65 35L67 35B30 76N10 35B40 35C07 PDF BibTeX XML Cite \textit{C. Shen} and \textit{M. Sun}, Z. Angew. Math. Phys. 64, No. 4, 1025--1056 (2013; Zbl 1272.35151) Full Text: DOI OpenURL
Diehl, Stefan Shock-wave behaviour of sedimentation in wastewater treatment: a rich problem. (English) Zbl 1421.76148 Åström, Kalle (ed.) et al., Analysis for science, engineering and beyond. The tribute workshop in honour of Gunnar Sparr, Lund, Sweden, May 8–9, 2008. Berlin: Springer. Springer Proc. Math. 6, 175-214 (2012). MSC: 76L05 76S05 PDF BibTeX XML Cite \textit{S. Diehl}, Springer Proc. Math. 6, 175--214 (2012; Zbl 1421.76148) Full Text: DOI OpenURL
Shen, Chun; Sun, Meina The bifurcation phenomenon for scalar conservation laws with discontinuous flux functions. (English) Zbl 1257.35128 Acta Appl. Math. 121, No. 1, 69-80 (2012). MSC: 35L67 35L65 35B30 76N10 PDF BibTeX XML Cite \textit{C. Shen} and \textit{M. Sun}, Acta Appl. Math. 121, No. 1, 69--80 (2012; Zbl 1257.35128) Full Text: DOI OpenURL
Andreianov, Boris; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik A theory of \(L ^{1}\)-dissipative solvers for scalar conservation laws with discontinuous flux. (English) Zbl 1261.35088 Arch. Ration. Mech. Anal. 201, No. 1, 27-86 (2011). Reviewer: Evgeniy Panov (Novgorod) MSC: 35L65 47H20 35A02 PDF BibTeX XML Cite \textit{B. Andreianov} et al., Arch. Ration. Mech. Anal. 201, No. 1, 27--86 (2011; Zbl 1261.35088) Full Text: DOI arXiv OpenURL
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 OpenURL
Wang, Guodong An Engquist-Osher type finite difference scheme with a discontinuous flux function in space. (English) Zbl 1230.65098 J. Comput. Appl. Math. 235, No. 17, 4966-4977 (2011). Reviewer: Petr Sváček (Praha) MSC: 65M06 65M12 35L65 35R05 PDF BibTeX XML Cite \textit{G. Wang}, J. Comput. Appl. Math. 235, No. 17, 4966--4977 (2011; Zbl 1230.65098) Full Text: DOI OpenURL
Wang, Guodong; Ge, Cishui Semidiscrete central-upwind scheme for conservation laws with a discontinuous flux function in space. (English) Zbl 1213.65127 Appl. Math. Comput. 217, No. 17, 7065-7073 (2011). MSC: 65M20 65M06 35L65 PDF BibTeX XML Cite \textit{G. Wang} and \textit{C. Ge}, Appl. Math. Comput. 217, No. 17, 7065--7073 (2011; Zbl 1213.65127) Full Text: DOI OpenURL
Adimurthi; Ghoshal, Shyam Sundar; Dutta, Rajib; Gowda, G. D. Veerappa Existence and nonexistence of TV bounds for scalar conservation laws with discontinuous flux. (English) Zbl 1223.35222 Commun. Pure Appl. Math. 64, No. 1, 84-115 (2011). MSC: 35L65 35R05 PDF BibTeX XML Cite \textit{Adimurthi} et al., Commun. Pure Appl. Math. 64, No. 1, 84--115 (2011; Zbl 1223.35222) Full Text: DOI OpenURL
Coclite, G. M.; Mishra, S.; Risebro, N. H. Convergence of an Engquist-Osher scheme for a multi-dimensional triangular system of conservation laws. (English) Zbl 1369.65108 Math. Comput. 79, No. 269, 71-94 (2010). MSC: 65M12 65M06 76S05 PDF BibTeX XML Cite \textit{G. M. Coclite} et al., Math. Comput. 79, No. 269, 71--94 (2010; Zbl 1369.65108) Full Text: DOI OpenURL
Mishra, Siddhartha; Jaffré, Jérôme On the upstream mobility scheme for two-phase flow in porous media. (English) Zbl 1398.76220 Comput. Geosci. 14, No. 1, 105-124 (2010). MSC: 76S05 76M12 76M20 35L65 35Q35 PDF BibTeX XML Cite \textit{S. Mishra} and \textit{J. Jaffré}, Comput. Geosci. 14, No. 1, 105--124 (2010; Zbl 1398.76220) Full Text: DOI arXiv OpenURL
Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik Well-balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation. (English) Zbl 1198.35149 Math. Comput. 78, No. 265, 55-78 (2009). MSC: 35L65 74S10 65M12 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., Math. Comput. 78, No. 265, 55--78 (2009; Zbl 1198.35149) Full Text: DOI OpenURL
Karlsen, K. H.; Mishra, S.; Risebro, N. H. Semi-Godunov schemes for multiphase flows in porous media. (English) Zbl 1191.35022 Appl. Numer. Math. 59, No. 9, 2322-2336 (2009). Reviewer: Argiris I. Delis (Chania) MSC: 35A35 65M60 35L65 35L45 65M12 76S05 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., Appl. Numer. Math. 59, No. 9, 2322--2336 (2009; Zbl 1191.35022) Full Text: DOI OpenURL
Diehl, Stefan A uniqueness condition for nonlinear convection-diffusion equations with discontinuous coefficients. (English) Zbl 1180.35305 J. Hyperbolic Differ. Equ. 6, No. 1, 127-159 (2009). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35K65 35L65 35R05 35A02 PDF BibTeX XML Cite \textit{S. Diehl}, J. Hyperbolic Differ. Equ. 6, No. 1, 127--159 (2009; Zbl 1180.35305) Full Text: DOI OpenURL
Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik Convergence of finite volume schemes for triangular systems of conservation laws. (English) Zbl 1190.65133 Numer. Math. 111, No. 4, 559-589 (2009). Reviewer: Yaşar Sözen (Istanbul) MSC: 65M12 65M06 35L65 76S05 76M12 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., Numer. Math. 111, No. 4, 559--589 (2009; Zbl 1190.65133) Full Text: DOI Link OpenURL
Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik A large-time-stepping scheme for balance equations. (English) Zbl 1133.76034 J. Eng. Math. 60, No. 3-4, 351-363 (2008). MSC: 76M12 76N15 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., J. Eng. Math. 60, No. 3--4, 351--363 (2008; Zbl 1133.76034) Full Text: DOI Link OpenURL
Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik Semi-Godunov schemes for general triangular systems of conservation laws. (English) Zbl 1133.76033 J. Eng. Math. 60, No. 3-4, 337-349 (2008). MSC: 76M12 76T30 76S05 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., J. Eng. Math. 60, No. 3--4, 337--349 (2008; Zbl 1133.76033) Full Text: DOI Link OpenURL
Bürger, R.; García, A.; Karlsen, K. H.; Towers, J. D. A family of numerical schemes for kinematic flows with discontinuous flux. (English) Zbl 1200.76126 J. Eng. Math. 60, No. 3-4, 387-425 (2008). MSC: 76M12 76T20 PDF BibTeX XML Cite \textit{R. Bürger} et al., J. Eng. Math. 60, No. 3--4, 387--425 (2008; Zbl 1200.76126) Full Text: DOI Link OpenURL
Coclite, Giuseppe Maria; Risebro, Nils Henrik Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients. (English) Zbl 1144.35016 J. Hyperbolic Differ. Equ. 4, No. 4, 771-795 (2007). MSC: 35F25 70H20 49L25 35L60 PDF BibTeX XML Cite \textit{G. M. Coclite} and \textit{N. H. Risebro}, J. Hyperbolic Differ. Equ. 4, No. 4, 771--795 (2007; Zbl 1144.35016) Full Text: DOI arXiv OpenURL
Adimurthi; Mishra, Siddhartha; Gowda, G. D. Veerappa Explicit Hopf-Lax type formulas for Hamilton-Jacobi equations and conservation laws with discontinuous coefficients. (English) Zbl 1128.35067 J. Differ. Equations 241, No. 1, 1-31 (2007). Reviewer: Nicolae Pop (Baia Mare) MSC: 35L65 49L25 35R05 PDF BibTeX XML Cite \textit{Adimurthi} et al., J. Differ. Equations 241, No. 1, 1--31 (2007; Zbl 1128.35067) Full Text: DOI OpenURL
Adimurthi; Mishra, Siddhartha; Veerappa Gowda, G. D. Conservation law with the flux function discontinuous in the space variable. II: Convex-concave type fluxes and generalized entropy solutions. (English) Zbl 1131.65071 J. Comput. Appl. Math. 203, No. 2, 310-344 (2007). Reviewer: Erwin Schechter (Moers) MSC: 65M06 65M12 35F25 35L65 PDF BibTeX XML Cite \textit{Adimurthi} et al., J. Comput. Appl. Math. 203, No. 2, 310--344 (2007; Zbl 1131.65071) Full Text: DOI OpenURL
Adimurthi; Mishra, Siddhartha; Gowda, G. D. Veerappa Convergence of Godunov type methods for a conservation law with a spatially varying discontinuous flux function. (English) Zbl 1116.35084 Math. Comput. 76, No. 259, 1219-1242 (2007). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 35L65 65M06 65M12 35L45 PDF BibTeX XML Cite \textit{Adimurthi} et al., Math. Comput. 76, No. 259, 1219--1242 (2007; Zbl 1116.35084) Full Text: DOI OpenURL
Herty, Michael; Seaïd, Mohammed; Singh, Anita K. A domain decomposition method for conservation laws with discontinuous flux function. (English) Zbl 1128.65078 Appl. Numer. Math. 57, No. 4, 361-373 (2007). Reviewer: Marek Brandner (Plzeň) MSC: 65M55 65M06 35L65 PDF BibTeX XML Cite \textit{M. Herty} et al., Appl. Numer. Math. 57, No. 4, 361--373 (2007; Zbl 1128.65078) Full Text: DOI OpenURL
Bürger, R.; Concha, F.; Karlsen, K. H.; Narváez, A. Numerical simulation of clarifier-thickener units treating ideal suspensions with a flux density function having two inflection points. (English) Zbl 1187.76759 Math. Comput. Modelling 44, No. 3-4, 255-275 (2006). MSC: 76T20 76M20 35L65 35Q35 PDF BibTeX XML Cite \textit{R. Bürger} et al., Math. Comput. Modelling 44, No. 3--4, 255--275 (2006; Zbl 1187.76759) Full Text: DOI OpenURL
Wang, Guodong; Sheng, Wancheng Interaction of elementary waves of scalar conservation laws with discontinuous flux function. (English) Zbl 1131.35363 J. Shanghai Univ. 10, No. 5, 381-387 (2006). MSC: 35L65 76N10 35L67 PDF BibTeX XML Cite \textit{G. Wang} and \textit{W. Sheng}, J. Shanghai Univ. 10, No. 5, 381--387 (2006; Zbl 1131.35363) Full Text: DOI OpenURL
Seaïd, Mohammed Stable numerical methods for conservation laws with discontinuous flux function. (English) Zbl 1088.65080 Appl. Math. Comput. 175, No. 1, 383-400 (2006). MSC: 65M06 65M12 35L65 90B20 76T10 65M25 PDF BibTeX XML Cite \textit{M. Seaïd}, Appl. Math. Comput. 175, No. 1, 383--400 (2006; Zbl 1088.65080) Full Text: DOI OpenURL
Adimurthi; Mishra, Siddhartha; Veerappa Gowda, G. D. Optimal entropy solutions for conservation laws with discontinuous flux-functions. (English) Zbl 1093.35045 J. Hyperbolic Differ. Equ. 2, No. 4, 783-837 (2005). Reviewer: Evgeniy Panov (Novgorod) MSC: 35L65 35L45 35B25 47J30 74S10 76M12 76S05 PDF BibTeX XML Cite \textit{Adimurthi} et al., J. Hyperbolic Differ. Equ. 2, No. 4, 783--837 (2005; Zbl 1093.35045) Full Text: DOI OpenURL
Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. A relaxation scheme for conservation laws with a discontinuous coefficient. (English) Zbl 1078.65076 Math. Comput. 73, No. 247, 1235-1259 (2004). Reviewer: Mária Lukáčová (Hamburg) MSC: 65M06 65M12 35L65 35L45 35R05 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., Math. Comput. 73, No. 247, 1235--1259 (2004; Zbl 1078.65076) Full Text: DOI OpenURL
Karlsen, K. H.; Risebro, N. H.; Towers, J. D. Front tracking for scalar balance equations. (English) Zbl 1053.35088 J. Hyperbolic Differ. Equ. 1, No. 1, 115-148 (2004). Reviewer: Mária Lukáčová (Hamburg) MSC: 35L60 35L45 76M25 35L65 35A35 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., J. Hyperbolic Differ. Equ. 1, No. 1, 115--148 (2004; Zbl 1053.35088) Full Text: DOI OpenURL
Berres, S.; Bürger, R.; Karlsen, K. H. Central schemes and systems of conservation laws with discontinuous coefficients modeling gravity separation of polydisperse suspensions. (English) Zbl 1107.76366 J. Comput. Appl. Math. 164-165, 53-80 (2004). MSC: 76M20 65M06 76E30 76T20 PDF BibTeX XML Cite \textit{S. Berres} et al., J. Comput. Appl. Math. 164--165, 53--80 (2004; Zbl 1107.76366) Full Text: DOI OpenURL
Zhang, Peng; Liu, Ru-Xun Hyperbolic conservation laws with space-dependent flux. I: Characteristics theory and Riemann problem. (English) Zbl 1031.35104 J. Comput. Appl. Math. 156, No. 1, 1-21 (2003). Reviewer: Messoud Efendiev (Berlin) MSC: 35L65 PDF BibTeX XML Cite \textit{P. Zhang} and \textit{R.-X. Liu}, J. Comput. Appl. Math. 156, No. 1, 1--21 (2003; Zbl 1031.35104) Full Text: DOI OpenURL
Bürger, R.; Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units. (English) Zbl 1013.35052 Nonlinear Anal., Real World Appl. 4, No. 3, 457-481 (2003). Reviewer: Thomas Sonar (Braunschweig) MSC: 35L65 65M99 86A05 PDF BibTeX XML Cite \textit{R. Bürger} et al., Nonlinear Anal., Real World Appl. 4, No. 3, 457--481 (2003; Zbl 1013.35052) Full Text: DOI OpenURL
Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik Unconditionally stable methods for Hamilton-Jacobi equations. (English) Zbl 1143.65365 J. Comput. Phys. 180, No. 2, 710-735 (2002). MSC: 65M06 35F25 PDF BibTeX XML Cite \textit{K. H. Karlsen} and \textit{N. H. Risebro}, J. Comput. Phys. 180, No. 2, 710--735 (2002; Zbl 1143.65365) Full Text: DOI OpenURL
Ostrov, Daniel N. Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependence. (English) Zbl 1009.35015 J. Differ. Equations 182, No. 1, 51-77 (2002). Reviewer: V.Iftode (Bucureşti) MSC: 35F25 PDF BibTeX XML Cite \textit{D. N. Ostrov}, J. Differ. Equations 182, No. 1, 51--77 (2002; Zbl 1009.35015) Full Text: DOI OpenURL
Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients. (English) Zbl 1032.76048 M2AN, Math. Model. Numer. Anal. 35, No. 2, 239-269 (2001). MSC: 76M20 76N15 65M06 35L65 PDF BibTeX XML Cite \textit{K. H. Karlsen} and \textit{N. H. Risebro}, M2AN, Math. Model. Numer. Anal. 35, No. 2, 239--269 (2001; Zbl 1032.76048) Full Text: DOI Numdam EuDML OpenURL
Klingenberg, Christian; Risebro, Nils Henrik Stability of a resonant system of conservation laws modeling polymer flow with gravitation. (English) Zbl 0977.35083 J. Differ. Equations 170, No. 2, 344-380 (2001). Reviewer: Evgeniy Panov (Novgorod) MSC: 35L65 76S05 PDF BibTeX XML Cite \textit{C. Klingenberg} and \textit{N. H. Risebro}, J. Differ. Equations 170, No. 2, 344--380 (2001; Zbl 0977.35083) Full Text: DOI Link OpenURL
Klausen, Runhild Aae; Risebro, Nils Henrik Stability of conservation laws with discontinuous coefficients. (English) Zbl 0935.35097 J. Differ. Equations 157, No. 1, 41-60 (1999). Reviewer: Mária Lukáčová (Brno) MSC: 35L65 35R05 PDF BibTeX XML Cite \textit{R. A. Klausen} and \textit{N. H. Risebro}, J. Differ. Equations 157, No. 1, 41--60 (1999; Zbl 0935.35097) Full Text: DOI OpenURL
Diehl, S.; Wallin, N.-O. Scalar conservation laws with discontinuous flux function. II: On the stability of the viscous profiles. (English) Zbl 0845.35068 Commun. Math. Phys. 176, No. 1, 45-71 (1996). Reviewer: L.G.Vulkov (Russe) MSC: 35L67 35L60 76S05 76T99 PDF BibTeX XML Cite \textit{S. Diehl} and \textit{N. O. Wallin}, Commun. Math. Phys. 176, No. 1, 45--71 (1996; Zbl 0845.35068) Full Text: DOI OpenURL
Diehl, S. Scalar conservation laws with discontinuous flux function. I: The viscous profile condition. (English) Zbl 0845.35067 Commun. Math. Phys. 176, No. 1, 23-44 (1996). Reviewer: L.G.Vulkov (Russe) MSC: 35L67 35L60 76S05 76T99 PDF BibTeX XML Cite \textit{S. Diehl}, Commun. Math. Phys. 176, No. 1, 23--44 (1996; Zbl 0845.35067) Full Text: DOI OpenURL
Klingenberg, Christian; Risebro, Nils Henrik Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior. (English) Zbl 0836.35090 Commun. Partial Differ. Equations 20, No. 11-12, 1959-1990 (1995). MSC: 35L65 35R05 35A05 35B40 PDF BibTeX XML Cite \textit{C. Klingenberg} and \textit{N. H. Risebro}, Commun. Partial Differ. Equations 20, No. 11--12, 1959--1990 (1995; Zbl 0836.35090) Full Text: DOI OpenURL