6,833 research outputs found
NonLocal Systems of Balance Laws in Several Space Dimensions with Applications to Laser Technolog
For a class of systems of nonlinear and nonlocal balance laws in several
space dimensions, we prove the local in time existence of solutions and their
continuous dependence on the initial datum. The choice of this class is
motivated by a new model devoted to the description of a metal plate being cut
by a laser beam. Using realistic parameters, solutions to this model obtained
through numerical integrations meet qualitative properties of real cuts.
Moreover, the class of equations considered comprises a model describing the
dynamics of solid particles along a conveyor belt
Smooth and discontinuous junctions in the p-system
Consider the p-system describing the subsonic flow of a fluid in a pipe with
section a = a(x). We prove that the resulting Cauchy problem generates a
Lipschitz semigroup, provided the total variation of the initial datum and the
oscillation of a are small. An explicit estimate on the bound of the total
variation of a is provided, showing that at lower fluid speeds, higher total
variations of a are acceptable. An example shows that the bound on TV(a) is
mandatory, for otherwise the total variation of the solution may grow
arbitrarily.Comment: 27 pages, 4 figure
Coupling conditions for the 3x3 Euler system
This paper is devoted to the extension to the full Euler system of
the basic analytical properties of the equations governing a fluid flowing in a
duct with varying section. First, we consider the Cauchy problem for a pipeline
consisting of 2 ducts joined at a junction. Then, this result is extended to
more complex pipes. A key assumption in these theorems is the boundedness of
the total variation of the pipe's section. We provide explicit examples to show
that this bound is necessary.Comment: 21 pages, 6 figure
Comparing methods of identify the appropriate sugar and pulp levels for fruit juice formulation: a consumer-driven approach.
Correction: Groundwater circulation and earthquake-related changes in hydrogeological karst environments: a case study of the Sibillini Mountains (central Italy) involving artificial tracers
The original version of this article was revised due to a retrospective Open Access order
A Waveguide Overloaded Cavity as Longitudinal Kicker for the daphne bunch-by-bunch Feedback System
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