Stability and Total Variation Estimates on General Scalar Balance Laws
By Rinaldo M. Colombo, M. Mercier, Massimiliano D. Rosini. 2008
52 citations recorded by the source corpus.
Consider the general scalar balance law @tu+Divf(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.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1d57677609ffa08cf72da50b68a086511a132e17
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In Applied Mathematics
In Control and Systems Engineering
- Magali L'ecureux-Mercier
- Rinaldo M. Colombo
- Mauro Garavello
- Michael Herty
- M. Mercier
- Paola Goatin
- Benedetto Piccoli
In Mathematical Physics
Citations in the corpus
- Nonlocal Crowd Dynamics Models for Several Populations (2011, methodology): “To extend all the above well posedness and stability results, we rely here essentially on [7], with the improvements in [14].”
- A CLASS OF NONLOCAL MODELS FOR PEDESTRIAN TRAFFIC (2011, methodology): “Using the techniques in [7, 9], we now obtain the continuous dependence of the solution to (1.”
- Control of the Continuity Equation with a Non Local Flow (2009, methodology): “Indeed, time derivatives of f appear in the proof of [15], Theorem 2.”