On the long-time limit of positive solutions to the degenerate logistic equation
On the long-time limit of positive solutions to the degenerate logistic equation
We study the long-time behavior of positive solutionsto the problem$u_t-\Delta u=a u-b(x)u^p \mbox{ in } (0,\infty)\times \Omega, Bu=0\mbox{ on } (0,\infty)\times \partial \Omega, $ where $a$ is areal parameter, $b\geq 0$ is in $C^\mu(\bar{\Omega})$ and $p>1$ is aconstant, $\Omega$ is a $C^{2+\mu}$ bounded domain in $R^N$ ($N\geq2$), the boundary operator …