{"id":{"repo_id":"claremont","oai_identifier":"oai:scholarship.claremont.edu:cgu_etd-2000"},"canonical_url":"https://search.dev.ndltd.org/etd/claremont/oai:scholarship.claremont.edu:cgu_etd-2000","repository":{"repo_id":"claremont","name":"Claremont Graduate University","base_url":"https://scholarship.claremont.edu/do/oai/"},"display":{"title":"Existence and Uniqueness of the Solution of a Traffic Flow Partial Differential Equation on Multi-Lane Freeways","abstract":"<p>In this dissertation, we shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when we apply the operator splitting method to the traffic flow stochastic partial differential equation.</p>","abstract_html":"&lt;p&gt;In this dissertation, we shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when we apply the operator splitting method to the traffic flow stochastic partial differential equation.&lt;/p&gt;","abstract_has_math":false,"creators":["Zareian, Sina"],"institution":null,"degree_name":"Mathematics, PhD","degree_level":"Open Access Dissertation","degree_discipline":"Institute of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Ali Nadim","Allon Percus"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-01-01T08:00:00Z","date_published":"2025-01-01T08:00:00Z","updated_at":"2026-07-24T01:41:09Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarship.claremont.edu/cgu_etd/978","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ali Nadim","Allon Percus"]},{"key":"dc:creator","label":"Author","values":["Zareian, Sina"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2025-05-09T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Institute of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics, PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarship.claremont.edu/cgu_etd/978"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>In this dissertation, we shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when we apply the operator splitting method to the traffic flow stochastic partial differential equation.</p>"]},{"key":"dc:title","label":"Title","values":["Existence and Uniqueness of the Solution of a Traffic Flow Partial Differential Equation on Multi-Lane Freeways"]}]}],"canonical_facts":{"dc:contributor":["Ali Nadim","Allon Percus"],"dc:creator":["Zareian, Sina"],"dc:date.available":["2025-05-09T07:00:00Z"],"dc:description.abstract":["<p>In this dissertation, we shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when we apply the operator splitting method to the traffic flow stochastic partial differential equation.</p>"],"dc:identifier":["https://scholarship.claremont.edu/cgu_etd/978"],"dc:subject":["Mathematics"],"dc:title":["Existence and Uniqueness of the Solution of a Traffic Flow Partial Differential Equation on Multi-Lane Freeways"],"thesis:degree_discipline":["Institute of Mathematical Sciences"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Mathematics, PhD"]},"updated_at":"2026-07-24T01:41:09Z"}