Keimer, Alexander; Pflug, Lukas Discontinuous nonlocal conservation laws and related discontinuous ODEs – existence, uniqueness, stability and regularity. (Lois de conservation non locales discontinues et ODE EDO discontinues correspondantes connexes – existence, unicité, stabilité et régularité.) (English. French summary) Zbl 07811835 C. R., Math., Acad. Sci. Paris 361, 1723-1760 (2023). MSC: 34A12 34A36 35L03 35L65 35Q99 35R09 45K05 PDFBibTeX XMLCite \textit{A. Keimer} and \textit{L. Pflug}, C. R., Math., Acad. Sci. Paris 361, 1723--1760 (2023; Zbl 07811835) Full Text: DOI arXiv
Bayen, Alexandre M.; Keimer, Alexander; Müller, Nils A proof of Kirchhoff’s first law for hyperbolic conservation laws on networks. (English) Zbl 07798681 Netw. Heterog. Media 18, No. 4, 1799-1819 (2023). MSC: 35R02 35L65 PDFBibTeX XMLCite \textit{A. M. Bayen} et al., Netw. Heterog. Media 18, No. 4, 1799--1819 (2023; Zbl 07798681) Full Text: DOI arXiv
Keimer, Alexander; Pflug, Lukas On the singular limit problem for a discontinuous nonlocal conservation law. (English) Zbl 1527.35172 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 237, Article ID 113381, 21 p. (2023). MSC: 35L65 35D30 35R09 34A36 PDFBibTeX XMLCite \textit{A. Keimer} and \textit{L. Pflug}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 237, Article ID 113381, 21 p. (2023; Zbl 1527.35172) Full Text: DOI arXiv
Coclite, Giuseppe Maria; Coron, Jean-Michel; De Nitti, Nicola; Keimer, Alexander; Pflug, Lukas A general result on the approximation of local conservation laws by nonlocal conservation laws: the singular limit problem for exponential kernels. (English) Zbl 07752596 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 40, No. 5, 1205-1223 (2023). Reviewer: Evgeniy Panov (Veliky Novgorod) MSC: 35L65 35R09 35B25 PDFBibTeX XMLCite \textit{G. M. Coclite} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 40, No. 5, 1205--1223 (2023; Zbl 07752596) Full Text: DOI arXiv
Bayen, Alexandre; Friedrich, Jan; Keimer, Alexander; Pflug, Lukas; Veeravalli, Tanya Modeling multilane traffic with moving obstacles by nonlocal balance laws. (English) Zbl 1497.35315 SIAM J. Appl. Dyn. Syst. 21, No. 2, 1495-1538 (2022). Reviewer: Giuseppe Maria Coclite (Bari) MSC: 35L45 35D30 35L65 35L03 76A30 PDFBibTeX XMLCite \textit{A. Bayen} et al., SIAM J. Appl. Dyn. Syst. 21, No. 2, 1495--1538 (2022; Zbl 1497.35315) Full Text: DOI
Bayen, Alexandre; Coron, Jean-Michel; De Nitti, Nicola; Keimer, Alexander; Pflug, Lukas Boundary controllability and asymptotic stabilization of a nonlocal traffic flow model. (English) Zbl 1471.35197 Vietnam J. Math. 49, No. 3, 957-985 (2021). MSC: 35L65 35L02 35L04 35L60 76A30 93C20 93B05 PDFBibTeX XMLCite \textit{A. Bayen} et al., Vietnam J. Math. 49, No. 3, 957--985 (2021; Zbl 1471.35197) Full Text: DOI
Keimer, Alexander; Singh, Manish; Veeravalli, Tanya Existence and uniqueness results for a class of nonlocal conservation laws by means of a Lax-Hopf-type solution formula. (English) Zbl 1478.35145 J. Hyperbolic Differ. Equ. 17, No. 4, 677-705 (2020). Reviewer: Evgeniy Panov (Veliky Novgorod) MSC: 35L65 35F21 35F31 35R09 PDFBibTeX XMLCite \textit{A. Keimer} et al., J. Hyperbolic Differ. Equ. 17, No. 4, 677--705 (2020; Zbl 1478.35145) Full Text: DOI
Leugering, Günter Partial differential equations on metric graphs: a survey of results on optimization, control, and stabilizability problems with special focus on shape and topological sensitivity problems. (English) Zbl 07357281 Manchanda, Pammy (ed.) et al., Mathematical modelling, optimization, analytic and numerical solutions. Selected papers based on the presentations at the international conference in conjunction with 14th biennial conference of ISIAM, Guru Nanak Dev University, Amritsar, India, February 2–4, 2018. Singapore: Springer. Ind. Appl. Math., 77-115 (2020). MSC: 34B45 35Q49 49Q10 81Q35 PDFBibTeX XMLCite \textit{G. Leugering}, in: Mathematical modelling, optimization, analytic and numerical solutions. Selected papers based on the presentations at the international conference in conjunction with 14th biennial conference of ISIAM, Guru Nanak Dev University, Amritsar, India, February 2--4, 2018. Singapore: Springer. 77--115 (2020; Zbl 07357281) Full Text: DOI
Coron, Jean-Michel; Keimer, Alexander; Pflug, Lukas Nonlocal transport equations – existence and uniqueness of solutions and relation to the corresponding conservation laws. (English) Zbl 1471.35250 SIAM J. Math. Anal. 52, No. 6, 5500-5532 (2020). Reviewer: Song Jiang (Beijing) MSC: 35Q49 35L03 35L65 35L67 76L05 35D30 35B35 35A01 35A02 90B20 PDFBibTeX XMLCite \textit{J.-M. Coron} et al., SIAM J. Math. Anal. 52, No. 6, 5500--5532 (2020; Zbl 1471.35250) Full Text: DOI
Keimer, Alexander; Pflug, Lukas Nonlocal conservation laws with time delay. (English) Zbl 1439.35325 NoDEA, Nonlinear Differ. Equ. Appl. 26, No. 6, Paper No. 54, 34 p. (2019). MSC: 35L65 35L03 65M25 PDFBibTeX XMLCite \textit{A. Keimer} and \textit{L. Pflug}, NoDEA, Nonlinear Differ. Equ. Appl. 26, No. 6, Paper No. 54, 34 p. (2019; Zbl 1439.35325) Full Text: DOI
Bayen, Alexandre; Keimer, Alexander; Porter, Emily; Spinola, Michele Time-continuous instantaneous and past memory routing on traffic networks: a mathematical analysis on the basis of the link-delay model. (English) Zbl 1432.34107 SIAM J. Appl. Dyn. Syst. 18, No. 4, 2143-2180 (2019). MSC: 34K60 90B20 92B20 PDFBibTeX XMLCite \textit{A. Bayen} et al., SIAM J. Appl. Dyn. Syst. 18, No. 4, 2143--2180 (2019; Zbl 1432.34107) Full Text: DOI
Keimer, Alexander; Pflug, Lukas On approximation of local conservation laws by nonlocal conservation laws. (English) Zbl 1428.35213 J. Math. Anal. Appl. 475, No. 2, 1927-1955 (2019). Reviewer: Jan Glaubitz (Braunschweig) MSC: 35L65 35Q91 90B20 PDFBibTeX XMLCite \textit{A. Keimer} and \textit{L. Pflug}, J. Math. Anal. Appl. 475, No. 2, 1927--1955 (2019; Zbl 1428.35213) Full Text: DOI
Keimer, Alexander; Leugering, Günter; Sarkar, Tanmay Analysis of a system of nonlocal balance laws with weighted work in progress. (English) Zbl 1437.35488 J. Hyperbolic Differ. Equ. 15, No. 3, 375-406 (2018). MSC: 35L65 35R09 PDFBibTeX XMLCite \textit{A. Keimer} et al., J. Hyperbolic Differ. Equ. 15, No. 3, 375--406 (2018; Zbl 1437.35488) Full Text: DOI
Keimer, Alexander; Pflug, Lukas; Spinola, Michele Nonlocal scalar conservation laws on bounded domains and applications in traffic flow. (English) Zbl 1404.35274 SIAM J. Math. Anal. 50, No. 6, 6271-6306 (2018). MSC: 35L04 35A01 35A02 35B09 35D30 35F31 35Q35 90B20 PDFBibTeX XMLCite \textit{A. Keimer} et al., SIAM J. Math. Anal. 50, No. 6, 6271--6306 (2018; Zbl 1404.35274) Full Text: DOI
Ancona, Fabio; Cesaroni, Annalisa; Coclite, Giuseppe M.; Garavello, Mauro On the optimization of conservation law models at a junction with inflow and flow distribution controls. (English) Zbl 1403.35166 SIAM J. Control Optim. 56, No. 5, 3370-3403 (2018). MSC: 35L65 35F25 90B20 35Q93 35R02 35D30 PDFBibTeX XMLCite \textit{F. Ancona} et al., SIAM J. Control Optim. 56, No. 5, 3370--3403 (2018; Zbl 1403.35166) Full Text: DOI arXiv
Cazacu, Cristian M.; Ignat, Liviu I.; Pazoto, Ademir F. Null-controllability of the linear Kuramoto-Sivashinsky equation on star-shaped trees. (English) Zbl 1393.35081 SIAM J. Control Optim. 56, No. 4, 2921-2958 (2018). MSC: 35K25 35R02 93B05 93B60 PDFBibTeX XMLCite \textit{C. M. Cazacu} et al., SIAM J. Control Optim. 56, No. 4, 2921--2958 (2018; Zbl 1393.35081) Full Text: DOI arXiv
Keimer, Alexander; Pflug, Lukas; Spinola, Michele Existence, uniqueness and regularity of multi-dimensional nonlocal balance laws with damping. (English) Zbl 1394.35275 J. Math. Anal. Appl. 466, No. 1, 18-55 (2018). MSC: 35L65 35L45 PDFBibTeX XMLCite \textit{A. Keimer} et al., J. Math. Anal. Appl. 466, No. 1, 18--55 (2018; Zbl 1394.35275) Full Text: DOI
Chalons, Christophe; Goatin, Paola; Villada, Luis M. High-order numerical schemes for one-dimensional nonlocal conservation laws. (English) Zbl 1387.35406 SIAM J. Sci. Comput. 40, No. 1, A288-A305 (2018). MSC: 35L65 90B20 76T20 65M08 65M60 PDFBibTeX XMLCite \textit{C. Chalons} et al., SIAM J. Sci. Comput. 40, No. 1, A288--A305 (2018; Zbl 1387.35406) Full Text: DOI arXiv
Keimer, Alexander; Pflug, Lukas Existence, uniqueness and regularity results on nonlocal balance laws. (English) Zbl 1372.35186 J. Differ. Equations 263, No. 7, 4023-4069 (2017). MSC: 35L65 35L03 65M25 35D30 35L45 PDFBibTeX XMLCite \textit{A. Keimer} and \textit{L. Pflug}, J. Differ. Equations 263, No. 7, 4023--4069 (2017; Zbl 1372.35186) Full Text: DOI
Chen, Wenbin; Liu, Chang; Wang, Zhiqiang Global feedback stabilization for a class of nonlocal transport equations: the continuous and discrete case. (English) Zbl 1368.35177 SIAM J. Control Optim. 55, No. 2, 760-784 (2017). MSC: 35L65 93C20 93D15 65M12 PDFBibTeX XMLCite \textit{W. Chen} et al., SIAM J. Control Optim. 55, No. 2, 760--784 (2017; Zbl 1368.35177) Full Text: DOI