%0 Journal Article
%T Asymptotic behavior of global solutions of the $u_t=¦¤u + u^{p}$
%A Oscar A. Barraza
%A Laura B. Langoni
%J Mathematics
%D 2008
%I arXiv
%X We study the asymptotic behavior of nonnegative solutions of the semilinear parabolic problem {u_t=\Delta u + u^{p}, x\in\mathbb{R}^{N}, t>0 u(0)=u_{0}, x\in\mathbb{R}^{N}, t=0. It is known that the nonnegative solution $u(t)$ of this problem blows up in finite time for $1<p\leq 1+ 2/N$. Moreover, if $p> 1+ 2/N$ and the norm of $u_{0}$ is small enough, the problem admits global solution. In this work, we use the entropy method to obtain the decay rate of the global solution $u(t)$.
%U http://arxiv.org/abs/0801.4798v1