Observation estimates for a semilinear heat equation in \mathbb{R}^n

This paper studies the state observation problems for the semilinear heat equation in R^n. We derive observation estimates for the equation using the logarithmic convexity property of the frequency function (see [12]). As an application, we show that if two solutions coincide on a nonempty open subset \omega\subset\Omega at some time T>0, then they must be identical.