Conservation laws with sharp inhomogeneities

Sharp L Stability Estimates for Hyperbolic Conservation Laws

Abstract. We introduce a generalization of Liu-Yang’s weighted norm to linear and to nonlinear hyperbolic equations. Following an approach due to the second author for piecewise constant solutions, we establish sharp L continuous dependence estimates for general solutions of bounded variation. Two different strategies are successfully investigated. On one hand, we justify passing to the limit i...

Conservation laws with discontinuous flux

We consider an hyperbolic conservation law with discontinuous flux. Such partial differential equation arises in different applicative problems, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic solutions...

Aggregation with multiple conservation laws.

Irreversible aggregation processes underly many natural phenomena including, e. g., polymerization [1], gelation [2], island growth [3-4] and aerosols [5]. The classical rate theory of Smoluchowski describes the kinetics of such processes [6-9]. Recently, scaling [10-16] and exact [17-23] theoretical studies showed that spatial correlations play a crucial role in low dimensions. While the above...

Conservation laws ,

We show that if performance measures in stochastic and dynamic scheduling problems satisfy generalized conservation laws, then the feasible space of achievable performance is a polyhedron called an extended polymatroid that generalizes the usual polymatroids introduced by Edmonds. Optimization of a linear objective over an extended polymatroid is solved by an adaptive greedy algorithm, which le...

Scaling laws and structural inhomogeneities in solids