One kind of unique continuation property for a wave equation is discussed. The authors show that, if one classical solution of the wave equation vanishes in an open set on a hyperplane, then it must vanish in a larger...One kind of unique continuation property for a wave equation is discussed. The authors show that, if one classical solution of the wave equation vanishes in an open set on a hyperplane, then it must vanish in a larger set on this hyperplane. The result can be viewed as a localized version of Robbiano’s result[9]. The approach involves the localized Fourier-Gauss transformation and unique continuation on a line in the Laplace equation.展开更多
文摘One kind of unique continuation property for a wave equation is discussed. The authors show that, if one classical solution of the wave equation vanishes in an open set on a hyperplane, then it must vanish in a larger set on this hyperplane. The result can be viewed as a localized version of Robbiano’s result[9]. The approach involves the localized Fourier-Gauss transformation and unique continuation on a line in the Laplace equation.
