Diffraction on a Cone: the Asymptotics of Solutions near the Vertex

AbstractThe paper is concerned with the mixed problem for the wave equation in a cone $$K \subset \mathbb{R}^n $$ . Asymptotic formulas for solutions and for the Green's function in a neighborhood of the vertex are obtained. Properties of the asymptotic coefficients related to a finite speed of propagation of disturbances are analyzed. Bibliography: 16 titles.