In this paper, we consider the dead core and some asymptotic behaviors of solutions to the initial boundary value problems of the equation u_t=△u-λupeu, where
Let φ be a normal function defined on [0, 1) and A~p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p【∞. The compactnesses of Toeplitz operaters