Initial value problem (IVP) for the BBM equation posed on the real line \(\mathbb {R}\) and on the torus \(\mathbb {T}\) with initial data that are analytic in a strip of width \(2\sigma _0\) in the complex plane is considered. It is known that the local solution preserves the radius of spatial analyticity during the time of existence; however, this radius may decrease as time evolves. In this work, we study the evolution of the radius of spatial analyticity \(\sigma (t)\) of the solution over time. For the BBM equation posed on the real line \(\mathbb {R}\) , by introducing appropriate damping terms, we show that the radius of spatial analyticity possesses a fixed positive lower bound uniformly in time. For the BBM equation posed on the periodic domain \(\mathbb {T}\) , first we show that the evolution of the radius of spatial analyticity cannot decay faster than \(ct^{-\frac{2}{3}}\) as the time t goes to infinity, improving the results obtained by Himonas and Petronilho (Proc Am Math Soc 148:2953–2967, 2020). Next, as in the real-line case, in this case too, the evolution of the radius of spatial analyticity is shown to be bounded below by a fixed constant by introducing damping terms.
