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

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Study on Systems of Nonlinear Conservation Laws Arising in Chemotaxis and Traffic Flow./
Author:	Mathur, Nitesh.
Description:	1 online resource (72 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
Contained By:	Dissertations Abstracts International85-01B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
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. - 1 online resource (72 pages)

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

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

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798379785734Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Balance lawsIndex Terms--Genre/Form:

554714
Electronic books.

Study on Systems of Nonlinear Conservation Laws Arising in Chemotaxis and Traffic Flow.
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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.
504 $a Includes bibliographical references
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Applied mathematics. $3 1069907
650 4 $a Theoretical mathematics. $3 1180455
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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710 2 $a The University of Iowa. $b Mathematics. $3 1466148
773 0 $t Dissertations Abstracts International $g 85-01B.
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