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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.

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > General Mathematics
Language:English
Date:June 2008
Deposited On:13 Jan 2009 07:31
Last Modified:01 Nov 2024 02:40
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/
OA Status:Green
Publisher DOI:https://doi.org/10.1142/S0219891608001544
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2420006
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