186 research outputs found
On the Stability Functional for Conservation Laws
This note is devoted to the explicit construction of a functional defined on
all pairs of \L1 functions with small total variation, which is equivalent to
the \L1 distance and non increasing along the trajectories of a given system
of conservation laws. Two different constructions are provided, yielding an
extension of the original stability functional by Bressan, Liu and Yang.Comment: 26 page
Modeling and analysis of pooled stepped chutes
We consider an application of pooled stepped chutes where the transport in
each pooled step is described by the shallow--water equations. Such systems can
be found for example at large dams in order to release overflowing water. We
analyze the mathematical conditions coupling the flows between different chutes
taken from the engineering literature. We present the solution to a Riemann
problem in the large and also a well--posedness result for the coupled problem.
We finally report on some numerical experiments.Comment: 17 pages, 31 figure
Balance laws with integrable unbounded sources
We consider the Cauchy problem for a strictly hyperbolic system
of balance laws each characteristic field being genuinely nonlinear or linearly
degenerate. Assuming that the norm of
and \|u_o\|_{BV(\reali)} are small enough, we
prove the existence and uniqueness of global entropy solutions of bounded total
variation extending the result in [1] to unbounded (in ) sources.
Furthermore, we apply this result to the fluid flow in a pipe with
discontinuous cross sectional area, showing existence and uniqueness of the
underlying semigroup.Comment: 26 pages, 4 figure
The Compressible to Incompressible Limit of 1D Euler Equations: the Non Smooth Case
We prove a rigorous convergence result for the compressible to incompressible
limit of weak entropy solutions to the isothermal 1D Euler equations.Comment: 16 page
Hyperbolic Balance Laws with a Dissipative Non Local Source
This paper considers systems of balance law with a dissipative non local
source. A global in time well posedness result is obtained. Estimates on the
dependence of solutions from the flow and from the source term are also
provided. The technique relies on a recent result on quasidifferential
equations in metric spaces.Comment: 17 page
Conservation Laws with Coinciding Smooth Solutions but Different Conserved Variable
Consider two hyperbolic systems of conservation laws in one space dimension
with the same eigenvalues and (right) eigenvectors. We prove that solutions to
Cauchy problems with the same initial data differ at third order in the total
variation of the initial datum. As a first application, relying on the
classical Glimm-Lax result, we obtain estimates improving those in by Saint
Raymond on the distance between solutions to the isentropic and non-isentropic
inviscid compressible Euler equations, under general equations of state.
Further applications are to the general scalar case, where rather precise
estimates are obtained, to an approximation by Di Perna of the p-system and to
a traffic model
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