Asymptotic behavior of global solutions of the $u_t=Δu + u^{p}$

Details Asymptotic behavior of global solutions of the $u_t=Δu + u^{p}$ Asymptotic behavior of global solutions of the $u_t=Δu + u^{p}$

2008-01-30

arxiv.org/abs/0801.4798v1

Mathematics

Analysis of PDEs

15

Scientific paper

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 $1 1+ 2/N$ 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 $u(t)$.

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