A MOMENT APPROACH FOR ENTROPY SOLUTIONS TO NONLINEAR HYPERBOLIC PDES

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00338416" target="_blank" >RIV/68407700:21230/20:00338416 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3934/mcrf.2019032" target="_blank" >https://doi.org/10.3934/mcrf.2019032</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/mcrf.2019032" target="_blank" >10.3934/mcrf.2019032</a>

Result language
angličtina
Original language name
A MOMENT APPROACH FOR ENTROPY SOLUTIONS TO NONLINEAR HYPERBOLIC PDES
Original language description
We propose to solve hyperbolic partial differential equations (PDEs) with polynomial flux using a convex optimization strategy. This approach is based on a very weak notion of solution of the nonlinear equation, namely the measure-valued (mv) solution, satisfying a linear equation in the space of Borel measures. The aim of this paper is, first, to provide the conditions that ensure the equivalence between the two formulations and, second, to introduce a method which approximates the infinite-dimensional linear problem by a hierarchy of convex, finite-dimensional, semidefinite programming problems. This result is then illustrated on the celebrated Burgers equation. We also compare our results with an existing numerical scheme, namely the Godunov scheme.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA16-19526S" target="_blank" >GA16-19526S: Semidefinite programming certification of control laws for emerging transportation projects</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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