Eternal solutions for a reaction-diffusion equation with weighted reaction
نویسندگان
چکیده
<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, $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>posed <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula>, id="M2">\begin{document}$ m&gt;1 id="M3">\begin{document}$ 0&lt;p&lt;1 $\end{document}</tex-math></inline-formula> critical value weight</p><p id="FE2"> \sigma \frac{2(1-p)}{m-1}. style='text-indent:20px;'>Existence some specific solution holds true when id="M4">\begin{document}$ m+p\geq2 $\end{document}</tex-math></inline-formula>. On contrary, no eternal exists if id="M5">\begin{document}$ m+p&lt;2 We also classify solutions a different interface behavior id="M6">\begin{document}$ m+p&gt;2 Some transformations to reaction-convection-diffusion equations traveling wave are introduced.</p>
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2022
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2021160