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Interaction of three progressing waves of higher order semilinear hyperbolic equations. (English) Zbl 0788.35092
Summary: The author gives an example to show the phenomenon of triple interaction for higher order semilinear hyperbolic systems. One obtains the result that when three characteristic hypersurfaces \(H_ 1\), \(H_ 2\), \(H_ 3\) carrying singularities intersect, singularities will propagate not only along \(H_ 1\), \(H_ 2\), \(H_ 3\), but also along the forward characteristic surfaces from \(H_ 1 \cap H_ 2\), \(H_ 2 \cap H_ 3\), \(H_ 3 \cap H_ 1\) and along the forward characteristic lightcone with vertex at \(H_ 1 \cap H_ 2 \cap H_ 3\). Furthermore, the orders of the anomalous singularities are given.
35L67 Shocks and singularities for hyperbolic equations
35L75 Higher-order nonlinear hyperbolic equations
35L55 Higher-order hyperbolic systems
35K20 Initial-boundary value problems for second-order parabolic equations