622 research outputs found
A new approach to transport equations associated to a regular field: trace results and well-posedness
We generalize known results on transport equations associated to a Lipschitz
field on some subspace of endowed with some general
space measure . We provide a new definition of both the transport operator
and the trace measures over the incoming and outgoing parts of generalizing known results from the literature. We also prove the
well-posedness of some suitable boundary-value transport problems and describe
in full generality the generator of the transport semigroup with no-incoming
boundary conditions.Comment: 30 page
Assembly of objects with not fully predefined shapes
An assembly problem in a non-deterministic environment, i.e., where parts to be assembled have unknown shape, size and location, is described. The only knowledge used by the robot to perform the assembly operation is given by a connectivity rule and geometrical constraints concerning parts. Once a set of geometrical features of parts has been extracted by a vision system, applying such a rule allows the dtermination of the composition sequence. A suitable sensory apparatus allows the control the whole operation
Non-autonomous Honesty theory in abstract state spaces with applications to linear kinetic equations
We provide a honesty theory of substochastic evolution families in real
abstract state space, extending to an non-autonomous setting the result
obtained for -semigroups in our recent contribution \textit{[On perturbed
substochastic semigroups in abstract state spaces, \textit{Z. Anal. Anwend.}
\textbf{30}, 457--495, 2011]}. The link with the honesty theory of perturbed
substochastic semigroups is established. Several applications to non-autonomous
linear kinetic equations (linear Boltzmann equation and fragmentation equation)
are provided
The role of regions and municipalities in the Italian multilevel governance of eldercare: recent trends in a context of increasing needs and budgetary constraints
open1Marco, ArlottiArlotti, Marc
Integral representation of the linear Boltzmann operator for granular gas dynamics with applications
We investigate the properties of the collision operator associated to the
linear Boltzmann equation for dissipative hard-spheres arising in granular gas
dynamics. We establish that, as in the case of non-dissipative interactions,
the gain collision operator is an integral operator whose kernel is made
explicit. One deduces from this result a complete picture of the spectrum of
the collision operator in an Hilbert space setting, generalizing results from
T. Carleman to granular gases. In the same way, we obtain from this integral
representation of the gain operator that the semigroup in L^1(\R \times \R,\d
\x \otimes \d\v) associated to the linear Boltzmann equation for dissipative
hard spheres is honest generalizing known results from the first author.Comment: 19 pages, to appear in Journal of Statistical Physic
An Lp -Approach to the Well-Posedness of Transport Equations Associated with a Regular Field: Part I
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