@Article{JPDE-35-307,
author = {Han , Junqiang},
title = {Doubly Nonlinear Degenerate Parabolic Equations with a Singular Potential for Greiner Vector Fields},
journal = {Journal of Partial Differential Equations},
year = {2022},
volume = {35},
number = {4},
pages = {307--319},
abstract = {<p style="text-align: justify;">The purpose of this paper is to investigate the nonexistence of positive solutions of the following doubly nonlinear degenerate parabolic equations: \begin{align*}\begin{cases}&nbsp; {\dfrac{\partial u}{\partial t}=\nabla_{k} \cdot \left( {u^{m-1}\left| {\nabla_{k} u} \right|^{p-2}\nabla_{k} u} \right)+V(w)u^{m+p-2}},\qquad &amp; {\mbox{in}\&nbsp; \Omega \times (0,T),} \\&nbsp; {u(w,0)=u_{0} (w)\geqslant 0}, &amp; {\mbox{in}\&nbsp; \Omega ,} \\&nbsp; {u(w,t)=0}, &amp; {\mbox{on}\&nbsp; \partial \Omega \times (0,T),}&nbsp; \end{cases} \end{align*} where $\Omega$ is a Carnot-Carathéodory metric ball in $\mathbb{R}^{2n+1}$ generated by Greiner vector fields, $V\in L_{loc}^{1} (\Omega )$, $k\in \mathbb{N}$, $m\in \mathbb{R}$, $1&lt;p&lt;2n+2k$ and $m+p-2&gt;0$. The better lower bound $p^*$ for $m + p_{ }$ is found and the nonexistence results are proved for $p^*\leqslant&nbsp; m+p&lt;3$.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v35.n4.1},
url = {http://global-sci.org/intro/article_detail/jpde/21050.html}
}