Colombo, Rinaldo M.; Mercier, Magali; Rosini, Massimiliano D. Stability and total variation estimates on general scalar balance laws. (English) Zbl 1183.35197 Commun. Math. Sci. 7, No. 1, 37-65 (2009). The authors consider the Cauchy problem for a multidimensional balance law \(\partial_t u+ \operatorname{Div} f(t,x,u)=F(t,x,u)\) and study dependence of the entropy solutions on the flow \(f\) and on the source \(F\). As a key intermediate result, the obtain a bound on the total variation of the solution. Applications of the obtained results are given to some balance laws with a nonlocal source inspired by the radiating gas model. Reviewer: Evgeniy Panov (Novgorod) Cited in 1 ReviewCited in 27 Documents MSC: 35L65 Hyperbolic conservation laws 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 76V05 Reaction effects in flows 35B35 Stability in context of PDEs 35L45 Initial value problems for first-order hyperbolic systems Keywords:Kruzhkov entropy solutions; total variation estimates; radiating gas model; nonlocal source PDFBibTeX XMLCite \textit{R. M. Colombo} et al., Commun. Math. Sci. 7, No. 1, 37--65 (2009; Zbl 1183.35197) Full Text: DOI arXiv