Let u(x,y,t) be the solution of the Cauchy problem
u_{tt}-c^2 u_{xx}-c^2 u_{yy}=0,
u(x,y,0)=f(x,y),
u_{t}(x,y,0)=g(x,y),

where c>0 is a constant and f(x,y) and g(x,y) vanish for x^2 +y^2 >r^2 for some r>0.
Show that the solution u(x,y,t) vanishes if x^2+y^2-r^2>c^2 t^2