A Class Of Ultra-parabolic Equation Observability Estimate

This paper is devoted to derive an observability inequality for the ultra-parabolic equations. Our method is based on first a point-wise and then a global Carleman-type estimates for an ultra-parabolic operator, which among other, yields a global unique continuation property for the solutions of a ultra-parabolic inequality, and also reproduces the known observability result for the heat equations.