An Observability Inequality On A Kind of Linear Parabolic Equation

Abstract

Abstract. In this paper, we study the observability inequality on a kind of linear parabolic equation.To show the observability estimate, we first derive the inequalities about the norms of the solution and its gradient, then reduce a lemma of inequality from a corollary directly [1]. At last, combing these inequalities with Nash inequality and Poincare inequality, we give the proof of the observability estimate.