Stability and Total Variation Estimates on General Scalar Balance Laws
Abstract
Consider the general scalar balance law ∂t u + f(t, x,u) = F(t,x,u) in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow f and from the source F. To this aim, a bound on the total variation in the space variables of the solution is obtained. This result is then applied to obtain well posedness and stability estimates for a balance law with a non local source.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.