Disputation: Markus Musch

Doctoral candidate Markus Musch at the Department of Mathematics will be defending the thesis Analysis and Numerical Treatment of Nonlinear Hyperbolic Conservation Laws on Graphs for the degree of Philosophiae Doctor.

picture of the candidate

Doctoral candidate Markus Musch

 

The PhD defence will be partially digital, in room 720, Niels Henrik Abels hus and streamed directly using Zoom. The host of the session will moderate the technicalities while the chair of the defence will moderate the disputation.

Ex auditorio questions: the chair of the defence will invite the audience to ask questions ex auditorio at the end of the defence. If you would like to ask a question, click 'Raise hand' and wait to be unmuted.

The webinar opens for participation just before the disputation starts, participants who join early will be put in a waiting room.

Trial lecture

19 of May, time: 02:00 pm, room 720 and Zoom.  

"Compensated compactness for conservation laws"
The webinar opens for participation just before the trial lecture starts, participants who join early will be put in a waiting room. 

Main research findings 

Hyperbolic conservation laws are used to model various important applications such as gas flow or traffic flow. Those phenomena are interesting to study in a one-dimensional setting, it would be even more relevant for real world applications, to study those equations on networks. Whilst the theory for hyperbolic conservation laws in 1D is fairly extensive, many questions are still open for the network case. My thesis addresses and solves several of these open questions.

In particular, my thesis addresses the question of well-posedness of hyperbolic conservation laws on networks. The question of well-posedness consists of three sub-questions, which are existence, uniqueness, and stability of a solution. In my thesis I present a fairly general well-posedness theory for a large class of equations that include models of gas flow and traffic flow on networks.

Furthermore, I developed a computer program that allows to compute approximate solutions to said equations and showed that this algorithm converges towards the actual solution. In addition to showing convergence of the algorithm, I also show results on how fast the algorithm converges towards the actual solution. This is important to know for computations of actual use cases.

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Adjudication committee

  • Professor of Mathematics Wen Shen, The Pennsylvania State University
  • Professeur des universités Nicolas Seguin, Université de Rennes 1
  • Professor Kenneth Aksel Hvistendahl Karlsen, University of Oslo

Supervisors

Chair of defence

Head of Department Geir Dahl

Host of the session

Professor Kenneth Aksel Hvistendahl Karlsen

    Candidate's contact information

    LinkedIn

    Organizer

    Department of Mathematics
    Published May 4, 2022 3:14 PM - Last modified May 10, 2022 10:25 AM