Interaction of progressing waves for semilinear wave equations. II. (English) Zbl 0653.35058

Melrose, Richard B.; Ritter, Niles

Ark. Mat. 25, 91-114 (1987).

[For part I, see Ann. Math., II. Ser. 121, 187-213 (1985; Zbl 0575.35063).]
From the authors’ summary: “This paper is related to the propagation of conormal regularity for solutions to semilinear wave equations, i.e. to the interaction of progressing waves for such an equation. One result of this type is proved here, for the wave operator in three dimensional space-time, concerning propagation of singularities associated to two or more characteristic surfaces, simply tangent along a common line. This special case is analysed in considerable detail for several reasons but principally to check the usefulness of different notions of regularity at such a singular variety. Three distinct spaces of iterated regularity associated to this geometry are investigated.”

Reviewer: A.D.Osborne

MSC:

35L67	Shocks and singularities for hyperbolic equations
35A20	Analyticity in context of PDEs
35L70	Second-order nonlinear hyperbolic equations
35B40	Asymptotic behavior of solutions to PDEs
35B65	Smoothness and regularity of solutions to PDEs

Keywords:

propagation of conormal regularity; semilinear; interaction of progressing waves; characteristic surfaces; singular variety; iterated regularity

Citations:

Zbl 0575.35063

References:

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