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

[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


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


Zbl 0575.35063
Full Text: DOI


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