Asymptotic laws for nonconservative self-similar fragmentations
نویسندگان
چکیده
We consider a self-similar fragmentation process in which the generic particle of mass x is replaced by the offspring particles at probability rate x, with positive parameter α. The total of offspring masses may be both larger or smaller than x with positive probability. We show that under certain conditions the typical mass in the ensemble is of the order t and that the empirical distribution of masses converges to a random limit which we characterise in terms of the reproduction law.
منابع مشابه
Asymptotics for the small fragments of the fragmentation at nodes
Abstract. We consider the fragmentation at nodes of the Lévy continuous random tree introduced in a previous paper. In this framework we compute the asymptotic for the number of small fragments at time θ. This limit is increasing in θ and discontinuous. In the α-stable case the fragmentation is self-similar with index 1/α, with α ∈ (1, 2) and the results are close to those Bertoin obtained for ...
متن کاملSelf-similar solutions of the Riemann problem for two-dimensional systems of conservation laws
In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem
متن کاملSelf-similar Fragmentations
We introduce a probabilistic model that is meant to describe an object that falls apart randomly as time passes and fulfills a certain scaling property. We show that the distribution of such a process is determined by its index of self-similarity , a rate of erosion c�0, and a so-called Lévy measure that accounts for sudden dislocations. The key of the analysis is provided by a transformation o...
متن کاملLarge-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws
In this paper we analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws. We consider three monotone conservative schemes that are consistent with the one-sided Lipschitz condition (OSLC): Lax-Friedrichs, Engquist-Osher and Godunov. We mainly focus on the inviscid Burgers equation, for which we know that the...
متن کاملNonconservative Noether’s Theorem in Optimal Control
We extend Noether’s theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the conserved quantities previously obtained in the literature for nonconservative problems of mechanics and the calculus of variations are derived.
متن کامل