{"id":27570,"date":"2026-03-24T18:58:58","date_gmt":"2026-03-24T10:58:58","guid":{"rendered":"https:\/\/cantor.math.ntnu.edu.tw\/?p=27570"},"modified":"2026-03-24T19:15:22","modified_gmt":"2026-03-24T11:15:22","slug":"lecture20260409","status":"publish","type":"post","link":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/2026\/03\/24\/lecture20260409\/","title":{"rendered":"<span style=\"color:#3566BD\">[\u5c08\u984c\u6f14\u8b1b] <\/span>\u30104\u67089\u65e5\u3011Helge Holden\uff0fMathematical modeling of traffic flow: Discrete vs Continuous"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"27570\" class=\"elementor elementor-27570\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ca442fe elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ca442fe\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6a1823f\" data-id=\"6a1823f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9a03688 elementor-widget elementor-widget-image\" data-id=\"9a03688\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"724\" height=\"1024\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/03\/20260409\u6d77\u5831\u632a\u5a01\u79d1\u5927Helge_Holdens-724x1024.png\" class=\"attachment-large size-large wp-image-27572\" alt=\"\" srcset=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/03\/20260409\u6d77\u5831\u632a\u5a01\u79d1\u5927Helge_Holdens-724x1024.png 724w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/03\/20260409\u6d77\u5831\u632a\u5a01\u79d1\u5927Helge_Holdens-212x300.png 212w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/03\/20260409\u6d77\u5831\u632a\u5a01\u79d1\u5927Helge_Holdens-768x1087.png 768w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2026\/03\/20260409\u6d77\u5831\u632a\u5a01\u79d1\u5927Helge_Holdens.png 793w\" sizes=\"(max-width: 724px) 100vw, 724px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b4a78da elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b4a78da\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-959f14e\" data-id=\"959f14e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c41627c elementor-widget elementor-widget-text-editor\" data-id=\"c41627c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong><span style=\"color: #000000;\">Abstract<\/span><\/strong><br \/><span style=\"color: #000000;\">Vehicular traffic is one of most serious problems facing modern urban life. We will describe some classical mathematical models for traffic flow. There are two rather distinct ways to model traffic. On the one hand one can track individual vehicles, often called Follow-the-Leader models (FtL). This leads to systems of ordinary differential equations. However, if traffic is dense, a classical model is the so-called Lighthill\u2013Whitham\u2013Richards model (LWR), which is a nonlinear partial differential equation, more specifically, a hyperbolic conservation law. We study these models, and, in particular, the connection between the discrete (FtL) and the continuous (LWR) when traffic becomes dense. We will also briefly discuss traffic on a network or roads, and traffic on multilane roads.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Abstract Vehicular traffic is one of most serious probl 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