05-123 Ismail Kombe
The Hardy inequality and Nonlinear parabolic equations on Carnot groups (399K, PS) Apr 4, 05
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Abstract. In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:$\begin{cases} \frac{\partial u}{\partial t}= \Delta_{\mathbb{G},p}u+V(x)u^{p-1} & \text{in}\quad \Omega \times (0, T ), \quad 1<p<2 ,\\ u(x,0)=u_{0}(x)\geq 0 & \text{in} \quad\Omega, \\ u(x,t)=0 & \text{on}\quad \partial\Omega\times (0, T) \end{cases}$ where $\Delta_{\mathbb{G},p}$ is the $p$-sub-Laplacian on Carnot group $\mathbb{G}$ and $V\in L_{\text{loc}}^1(\Omega)$.

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