Asymptotic behavior of Green function for a parabolic equation associated to a Dirichlet form on metric spaces.

  • Tarek Kenzizi

Abstract


In this paper, we are interesting by the asymptotic behavior of Green function for the parabolic problem
\begin{equation}
\left\{
\begin{array}{ll}
H u - V u + \frac{\partial u}{\partial t} =0,\quad \hbox{in } X\times \mathbb{R}_{+},\\
u(x,0)= u_{0}(x),~~x\in X .
\end{array}
\right.
\end{equation}
where $u_{0}\in L^{2}(X,m)$, $X$ is a complete locally compact metric space, $H$ is a selfadjoint operator associated with a regular Dirichlet form $\mathcal E$ and $m$ is a Radon measure on non-empty Borel subspace $U$ of $X$ such that $m(U)>0$ and $V$ belongs to a class of time dependant potentials which can be written as a nonlinear combination of derivatives functions.

Published
Nov 26, 2017
How to Cite
KENZIZI, Tarek. Asymptotic behavior of Green function for a parabolic equation associated to a Dirichlet form on metric spaces.. Nonlinear Studies, [S.l.], v. 24, n. 4, p. 805-823, nov. 2017. ISSN 2153-4373. Available at: <http://nonlinearstudies.com/index.php/nonlinear/article/view/1228>. Date accessed: 15 dec. 2017.