Uniqueness In Boundary Value Problems For The Second Order Hyperbolic Equation

Abstract

Introduction. We study linear normal hyperbolic partial differential equations of the second order, with one dependent variable u, and N independent variables xⁱ (i = 1, … , N). The uniqueness theorem connected with the Cauchy problem for this type of equation is well known and in effect states that if u and its first normal derivatives vanish on a spacelike initial surface S then u vanishes in a certain conical region which contains S (1, p. 379).