Interactions involving gliding rays in boundary problems for semilinear wave equations (Q1812881)

The author studies the spreading of singularities and the strength of anomalous singularities for the Dirichlet problem for a semilinear wave equation. The case of singularity-bearing refecting rays has been examined in previous work of the author [Trans. Am. Math. Soc. 311, 291- 321 (1989; Zbl 0701.58055)]. Here the aim is to examine the case when we have an interaction involving at least one gliding ray. One considers the following cases: (a) self-spreading of a gliding ray; (b) crossing of two gliding rays; (c) crossing of a gliding ray and a reflecting ray. In all these cases precise results about the strength of the singularities produced are given.