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Study on Systems of Nonlinear Conservation Laws Arising in Chemotaxis and Traffic Flow.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Study on Systems of Nonlinear Conservation Laws Arising in Chemotaxis and Traffic Flow.
Author:	Mathur, Nitesh.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2023
Description:	72 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
Notes:	Advisor: Li, Tong.
Contained By:	Dissertations Abstracts International85-01B.
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30417676
ISBN:	9798379785734

Study on Systems of Nonlinear Conservation Laws Arising in Chemotaxis and Traffic Flow.
Mathur, Nitesh.

Study on Systems of Nonlinear Conservation Laws Arising in Chemotaxis and Traffic Flow. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 72 p.

Source: Dissertations Abstracts International, Volume: 85-01, Section: B.

Thesis (Ph.D.)--The University of Iowa, 2023.

This item must not be sold to any third party vendors.

We study nonlinear conservation laws in partial differential equations (PDEs). In particular, we investigate systems of conservation laws in biology and traffic flow. We solve the Riemann problem for a system modeling chemotaxis and prove the existence of global BV solutions to the Cauchy problem for a system of balance laws arising in traffic flow.For our first problem, we study the Riemann problem for a system arising in chemotaxis. The system is of mixed-type and transitions from a hyperbolic to an elliptic region. We solve the Riemann problem in the physically relevant region up to the non-strictly boundary that occurs between the hyperbolic and elliptic regions. While solving this problem, we encounter classical shock and rarefaction waves in the hyperbolic region as well as contact discontinuities in the linearly degenerate region.For the second problem, we establish global well-posedness and asymptotic behavior of BV solutions to a system of balance laws modeling traffic flow with nonconcave fundamental diagram. This problem is of specific interest since nonconcave fundamental diagrams arise naturally in traffic flow. We prove the results for the system with concave fundamental diagram by finding a convex entropy-entropy flux pair and verifying the Kawashima condition, the sub-characteristic condition, and the partial dissipative inequality in the framework of Dafermos. We then extend the results to nonconcave fundamental diagram by perturbation analysis.

ISBN: 9798379785734Subjects--Topical Terms:

184409
Mathematics.
Subjects--Index Terms:

Balance laws

Study on Systems of Nonlinear Conservation Laws Arising in Chemotaxis and Traffic Flow.
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100 1 $a Mathur, Nitesh. $3 966810
245 1 0 $a Study on Systems of Nonlinear Conservation Laws Arising in Chemotaxis and Traffic Flow.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 72 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
500 $a Advisor: Li, Tong.
502 $a Thesis (Ph.D.)--The University of Iowa, 2023.
506 $a This item must not be sold to any third party vendors.
520 $a We study nonlinear conservation laws in partial differential equations (PDEs). In particular, we investigate systems of conservation laws in biology and traffic flow. We solve the Riemann problem for a system modeling chemotaxis and prove the existence of global BV solutions to the Cauchy problem for a system of balance laws arising in traffic flow.For our first problem, we study the Riemann problem for a system arising in chemotaxis. The system is of mixed-type and transitions from a hyperbolic to an elliptic region. We solve the Riemann problem in the physically relevant region up to the non-strictly boundary that occurs between the hyperbolic and elliptic regions. While solving this problem, we encounter classical shock and rarefaction waves in the hyperbolic region as well as contact discontinuities in the linearly degenerate region.For the second problem, we establish global well-posedness and asymptotic behavior of BV solutions to a system of balance laws modeling traffic flow with nonconcave fundamental diagram. This problem is of specific interest since nonconcave fundamental diagrams arise naturally in traffic flow. We prove the results for the system with concave fundamental diagram by finding a convex entropy-entropy flux pair and verifying the Kawashima condition, the sub-characteristic condition, and the partial dissipative inequality in the framework of Dafermos. We then extend the results to nonconcave fundamental diagram by perturbation analysis.
590 $a School code: 0096.
650 4 $a Mathematics. $3 184409
650 4 $a Applied mathematics. $3 377601
650 4 $a Theoretical mathematics. $3 708655
653 $a Balance laws
653 $a Chemotaxis
653 $a Global BV Solutions
653 $a Riemann problem
653 $a Conservation laws
653 $a Traffic flow
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690 $a 0364
690 $a 0642
710 2 $a The University of Iowa. $b Mathematics. $3 966811
773 0 $t Dissertations Abstracts International $g 85-01B.
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791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30417676