Null Controllability for the Dissipative Semilinear Heat Equation

Abstract. We consider the exact null controllability problem for the semi- linear heat equation with dissipative nonlinearity in a bounded domain of Rn . The main result of the article asserts that if the nonlinearity is even mildly superlinear, then global null controllability in an arbitrarily short time fails; instead we provide sharp estimates for the controllability time in terms of the size of the initial data.