×

Stability and total variation estimates on general scalar balance laws. (English) Zbl 1183.35197

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.

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
PDFBibTeX XMLCite
Full Text: DOI arXiv