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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.
##### MSC:
 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