Zur Abhängigkeit der Lösung von ut + (h(u))x = 0 von ihren Anfangswerten

The above equation has some remarkable properties. In general a global solution exists in a weak sense only, and this solution is not reversible in time. Furthermore it is known, that the solutions for different initial values can coincide for all t ? t₀ > 0, and the set of the initial values with this property is convex. Conditions assuring that this set contains only one element are given. This means a weak form of time-reversibility. As a global solution exists only in the weak sense, the classical question concerning dependence of the solution on the initial values needs some modification. This problem is dealt with in suitable L₁-norms. It is shown, that the L₁-norm of the difference of two weak solutions with respect to the space variable does not increase in time.