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Project Euclid
Other literature type . 2002
Data sources: Project Euclid
Current Developments in Mathematics
Article . 2002 . Peer-reviewed
Data sources: Crossref
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One dimensional hyperbolic systems of conservation laws

Authors: Bressan, Alberto;

One dimensional hyperbolic systems of conservation laws

Abstract

These notes are meant to provide a survey of some recent results and techniques in the theory of conservation laws. In one space dimension, a system of conservation laws can be written as ut + f(u) x = 0. Here u = (u1, ... , un) is the vector of conserved quantities while the components of f = (f1, ... , fn) are called the fluxes. Integrating over the interval [a, b] one obtains d/dt ?ab u(t,x) dx = ?ab ut(t,x) dx = - ?ab f( u(t,x))x dx = f(u(t,a)) - f(u(t,b)) = [inflow at a ] - outflow at b]. In other words, each component of the vector u represents a quantity which is neither created nor destroyed: its total amount inside any given interval [a, b] can change only because of the flow across boundary points.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Average
Top 10%
Average
Green
bronze