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Abstract
A systematic study is made of the general behaviour of solutions to the Bernoulli equation which governs the evolution of acceleration waves in nonlinear systems. The theorems obtained contain all the known results and, in some instances, when specialized to the case of an existing theorem they provide a sharper results obtained here for the Bernoulli equation, and the corresponding results for the propagation of weak discontinuity in a general quasilinear hyperbolic system