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Structure preserving schemes and kinetic models for approximating measure valued solutions of hyperbolic equations

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posted on 2023-06-09, 22:53 authored by Ioannis Gkanis
In this thesis we consider approximate schemes and models for hyperbolic conservation laws. Systems of conservation laws are fundamental mathematical models and have received a lot of attention from the point of view of analysis, modelling and computations. They include the wave equations in elastic media and fundamental equations in fluid mechanics. We consider structure preserving schemes and kinetic models for approximating measure valued solutions of hyperbolic equations. Such solutions are of interest given their application to problems in uncertainty quantification and in statistical inference. This thesis contains new results on (i) the design of new schemes for the computation of entropy consistent approximations, with particular emphasis on the consistency of the computational algorithms to entropic measure valued solutions for HCL, (ii) the introduction of discrete and generalised kinetic models designed to directly approximate measure valued solutions by using a combination of approximate Young measures and the kinetic formulation of the conservation law and (iii) stability analysis of generalised viscus kinetic models. We obtain uniqueness within a particular class of vanishing viscosity limits of these models and of their corresponding measure valued solutions.

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  • Published version

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137.0

Department affiliated with

  • Mathematics Theses

Qualification level

  • doctoral

Qualification name

  • phd

Language

  • eng

Institution

University of Sussex

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  • Yes

Legacy Posted Date

2021-01-25

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