05-123 Ismail Kombe

The Hardy inequality and Nonlinear parabolic equations on Carnot groups (399K, PS) Apr 4, 05

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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 $V\in L_{\text{loc}}^1(\Omega)$.

Files: 05-123.src( 05-123.keywords , carnotp-laplacekom.ps )