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TRAVELING WAVES OF A NON-LOCAL CONSERVATION LAW

Yu, Yan (2011) TRAVELING WAVES OF A NON-LOCAL CONSERVATION LAW. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

This dissertation establishes the existence and uniqueness of the traveling waves related to shocks for a non-local scalar conservation law u_t + (f(u))_x = K * u - u, where f is an arbitrary continuous differentiable function, K * u stands for the convolution in the spatial variable x, and K is an arbitrary non-negative kernel with unit mass not necessary centered at the origin and with bounded first moment. We first truncate the problem from the real line R to a finite domain and then add an artificial viscosity so that the problem becomes a second-order elliptic boundary value problem. Utilizing classical techniques, we establish the existence and uniqueness of the boundary value problem. Then we send the boundary points to infinity to extend the result to the whole real line. Finally we send the viscosity to zero and show that the limit is the traveling wave solution to the non-local scalar conservation law problem.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Yu, Yanmsyanyu@gmail.com
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChen, Xinfuxinfu@pitt.eduXINFU
Committee MemberLeoni, Giovannigiovanni@andrew.cmu.edu
Committee MemberHastings, Stuartsph@pitt.eduSPH
Committee MemberTroy, Williamtroy@math.pitt.eduTROY
Date: 31 January 2011
Date Type: Completion
Defense Date: 8 November 2010
Approval Date: 31 January 2011
Submission Date: 17 November 2010
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Applied Mathematics; Conservation Law; Ordinary Differential Equations; Partial Differential Equations; Perturbed Convection-Diffusion Problem; Traveling Wave; Truncation Method
Other ID: http://etd.library.pitt.edu/ETD/available/etd-11172010-215908/, etd-11172010-215908
Date Deposited: 10 Nov 2011 20:05
Last Modified: 15 Nov 2016 13:51
URI: http://d-scholarship.pitt.edu/id/eprint/9708

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