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

### 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.
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