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Asymptotic behavior of solutions for some semilinear heat equations in $R^N$
| 1. | Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan, Japan |
$\partial_t u = \Delta u +f(u)$ in $R^N \times (0,\infty),$
$u (x,0) = \phi (x) \ge 0$ in $R^N,\quad\quad$
where $N \geq 1$, $f \in C^1([0,\infty))$, and $\phi \in L^1(R^N) \cap L^{\infty}(R^N)$. We study the asymptotic behavior of the solutions in the $L^q$ spaces with $q \in [1,\infty]$, by using the relative entropy methods.
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