<p style='text-indent:20px;'>We prove existence and uniqueness of <i>eternal solutions</i> in self-similar form growing up time with exponential rate for the weighted reaction-diffusion equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \partial_tu = \Delta u^m+|x|^{\sigma}u^p, $\end{document} &l...