| Contents |
| We consider a parabolic equation of the form
\begin{equation*}
\begin{gathered}
u_t=\Delta u +f(u)+h(x,t),\quad (x,t)\in\mathbb R^N\times (0,\infty)\\
u(x,t)\ge 0\quad\mbox{for all }(x,t)\in\mathbb R^N\times (0,\infty).
\end{gathered}
\end{equation*}
where $f\in C^1(\mathbb R)$ is such that $f(0)=0$, $f'(0)$ negative and $h$ is a suitable function on $\mathbb R^N\times (0,\infty)$. We show that under certain conditions, each globally defined and nonnegative bounded solution $u$ converges to a single steady state. |
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