By Symon, K.R.; Argonne National Lab.; United States. Dept. of Energy. Office of Energy Research.; United States. Dept. of Energy. Office of Scientific and Technical Information

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However careful reading shows that there too only the former statement can be justified. 1) which can be obtained from the study of the integral equation (1. 9). 1 Admissible wave speeds Our first result states that the set of speeds for which such a solution decreasing to 0 exists is either empty, or, connected and unbounded above. 1. 1) has a semi-wavefront solution with speed aD decreasing to 0, then the equation has such a solution for every wave speed a ~ aD. 18. 1) implies the existence of such a solution for another equation of the same type.

Noting that in the Burgers equation the unknown u denotes a variable which is a measure of turbulence in hydrodynamic flow, the inference of the positivity of the semi-wavefront solutions is that in it is impossible to have regions with turbulence in combination with regions where there is no dissipation of energy. 7) Modelling the motion of a foam composed of gas bubbles trapped in a liquid in one spatial dimension, the unknown in this equation denotes the liquid fraction of the foam, t time, and, x a spatial coordinate.

6(i) implies that u 2 2': 4A. 24) we may therefore suppose that A < u 2/4 without loss of generality. 29) where f31 := (u - vu 2 - 4A)/2 and f32 := (u + vu 2 - 4A)/2. Furthermore if [0,8""'() denotes its maximal interval of existence contained in [0,8), 0""'( is positive on (0,8""'(),8""'( depends continuously and monotonically on "I, and, 8""'( --7 0 as "I --7 -00.

### Derivation of Hamiltonians for accelerators by Symon, K.R.; Argonne National Lab.; United States. Dept. of Energy. Office of Energy Research.; United States. Dept. of Energy. Office of Scientific and Technical Information

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