UZH-Logo

Maintenance Infos

SBV regularity of entropy solutions for a class of genuinely nonlinear scalar balance laws with non-convex flux function


Robyr, R (2008). SBV regularity of entropy solutions for a class of genuinely nonlinear scalar balance laws with non-convex flux function. Journal of Hyperbolic Differential Equations, 5(2):449-475.

Abstract

In this work we study the regularity of entropy solutions of the genuinely nonlinear scalar balance laws

We assume that the source term g ∈ C1(ℝ × ℝ × ℝ+), that the flux function f ∈ C2(ℝ × ℝ × ℝ+) and that {ui ∈ ℝ : fuu(ui,x,t) = 0} is at most countable for every fixed (x,t) ∈ Ω. Our main result, which is a unification of two proposed intermediate theorems, states that BV entropy solutions of such equations belong to SBVloc(Ω). Moreover, using the theory of generalized characteristics we prove that for entropy solutions of balance laws with convex flux function, there exists a constant C > 0 such that:

where C can be chosen uniformly for (x +h,t), (x,t) in any compact subset of Ω.

Abstract

In this work we study the regularity of entropy solutions of the genuinely nonlinear scalar balance laws

We assume that the source term g ∈ C1(ℝ × ℝ × ℝ+), that the flux function f ∈ C2(ℝ × ℝ × ℝ+) and that {ui ∈ ℝ : fuu(ui,x,t) = 0} is at most countable for every fixed (x,t) ∈ Ω. Our main result, which is a unification of two proposed intermediate theorems, states that BV entropy solutions of such equations belong to SBVloc(Ω). Moreover, using the theory of generalized characteristics we prove that for entropy solutions of balance laws with convex flux function, there exists a constant C > 0 such that:

where C can be chosen uniformly for (x +h,t), (x,t) in any compact subset of Ω.

Citations

9 citations in Web of Science®
10 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

29 downloads since deposited on 13 Jan 2009
1 download since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:June 2008
Deposited On:13 Jan 2009 07:31
Last Modified:05 Apr 2016 12:43
Publisher:World Scientific Publishing
ISSN:0219-8916
Additional Information:Electronic version of an article published as Journal of Hyperbolic Differential Equations, 5(2):449-475 (2008). Article DOI: 10.1142/S0219891608001544 © 2008 copyright World Scientific Publishing Company, http://www.worldscinet.com/jhde/
Publisher DOI:https://doi.org/10.1142/S0219891608001544
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2420006

Download

[img]
Preview
Content: Accepted Version
Filetype: PDF
Size: 361kB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations