
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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