A uniqueness theorem for the reduced wave equation

An existence theorem for the reduced wave equation

“…where Tí* denotes the zero order Hankel function of the first kind. Then for fixed z0 and z^z0 Q satisfies (1) and (2). For small r we have…”

Curves along which plane waves can interfere

“…A corollary of the conjecture is that for the Dirichlet problem it is impossible to avoid having a scattered field when the incident field consists of an odd number of plane waves. Conversely, it is known that if the incident field is zero for a smooth finite arc then the field scattered off the arc is zero [3].…”

An Existence Theorem for the Reduced Wave Equation

“…We assume that the functions x¿(í) and y((t) have Holder continuous second derivatives and that the arcs £,-do not intersect. We denote the union of the £,'s by £ and the open set £2 -£ by G. We seek a function u,(x, y) which satisfies the following conditions: Uniqueness follows from the work of Levine [2]. (Levine proves his uniqueness theorem in the three dimensional case, however his proof can easily be modified so as to apply here.)…”

“…Uniqueness follows from the work of Levine [2]. (Levine proves his uniqueness theorem in the three dimensional case, however his proof can easily be modified so as to apply here.)…”