One-dimensional scalar conservation laws with regulated data

Helge Kristian Jenssen; Johanna Ridder

doi:10.1137/19M1267957

One-dimensional scalar conservation laws with regulated data

Helge Kristian Jenssen, Johanna Ridder

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We show that the Kružkov solution of the Cauchy problem for a scalar conservation law in one spatial dimension propagates regulated initial data into regulated solutions at later times. The proof is based on standard front-tracking and an extension, due to Fraňková, of Helly's selection principle.

Original language	English (US)
Pages (from-to)	3114-3130
Number of pages	17
Journal	SIAM Journal on Mathematical Analysis
Volume	52
Issue number	3
DOIs	https://doi.org/10.1137/19M1267957
State	Published - 2020

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/19M1267957

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title = "One-dimensional scalar conservation laws with regulated data",

abstract = "We show that the Kru{\v z}kov solution of the Cauchy problem for a scalar conservation law in one spatial dimension propagates regulated initial data into regulated solutions at later times. The proof is based on standard front-tracking and an extension, due to Fra{\v n}kov{\'a}, of Helly's selection principle.",

author = "Jenssen, {Helge Kristian} and Johanna Ridder",

note = "Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics.",

year = "2020",

doi = "10.1137/19M1267957",

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volume = "52",

pages = "3114--3130",

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AU - Jenssen, Helge Kristian

AU - Ridder, Johanna

PY - 2020

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AB - We show that the Kružkov solution of the Cauchy problem for a scalar conservation law in one spatial dimension propagates regulated initial data into regulated solutions at later times. The proof is based on standard front-tracking and an extension, due to Fraňková, of Helly's selection principle.

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AN - SCOPUS:85091341318

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EP - 3130

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 3

ER -

One-dimensional scalar conservation laws with regulated data

Abstract

All Science Journal Classification (ASJC) codes

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