Well posedness for differential inclusions on closed sets

Epi-Lipschitzian reachable sets of differential inclusions

The reachable sets of a differential inclusion have nonsmooth topological boundaries in general. The main result of this paper is that under the well–known assumptions of Filippov’s existence theorem (about solutions of differential inclusions), every epi-Lipschitzian initial compact set K ⊂ RN preserves this regularity for a short time, i.e. θF (t, K) is also epi-Lipschitzian for all small t >...

On The Solution Sets Of Semicontinuous Quantum Stochastic Differential Inclusions∗

The aim of this paper is to provide a unified treatment of the existence of solution of both upper and lower semicontinuous quantum stochastic differential inclusions. The quantum stochastic differential inclusion is driven by operatorvalued stochastic processes lying in certain metrizable locally convex space. The unification of solution sets to these two discontinuous non-commutative stochast...

Partially Well-Ordered Closed Sets of Permutations

It is known that the \pattern containment" order on permutations is not a partial well-order. Nevertheless, many naturally de ned subsets of permutations are partially well-ordered, in which case they have a strong nite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains are exhibited that give some insight as...

Well-posedness for Hall-magnetohydrodynamics

We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resitive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions. Acknowledgements: The first and third authors wish to thank the hospitality of the Institut de Mathématiques de Toulouse, France, where this research has been car...

Well-posedness for Hyperbolic Problems