Wave Equations in a Complex Domain

J. Math. Sci. Univ. Tokyo
Vol. 23 (2016), No. 2, Page 405--423.

Uchikoshi, Keisuke
Wave Equations in a Complex Domain
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We consider Cauchy problems for 2-dimensional wave equations in a complex domain. We assume that the initial values have singularities along the union of two hypersurfaces which are normally crossing at the origin. We show that the solutions have singularities not only along the corresponding characteristic hypersurfaces but also on the light cone issuing from the origin.

Keywords: Complex Cauchy propblem, propagation of the singularities, light cone.

Mathematics Subject Classification (2010): Primary 35L05; Secondary 35A20, 35A21.
Mathematical Reviews Number: MR3469004

Received: 2013-08-19