Abstract
Abstract A two-stage analysis do detect the appearance of a gradient catastrophe of the solution is proposed for quasilinear systems of hyperbolic equations of special form. Applications of the first stage are considered for the following simple cases: scalar Burgers’ equation and a quasi-orthogonal system generalizing it. The entire two-stage analysis is applied to systems of equations describing one-dimensional electron oscillations in plasma, namely, plane oscillations in the relativistic and non-relativistic cases and also axially symmetric non-relativistic cylindrical oscillations.
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