  Here we study the initial trace problem for the nonnegative solutions of the
equation \[ u\_{t}-\Delta u+|\nabla u|^{q}=0 \] in
$Q\_{\Omega,T}=\Omega\times\left( 0,T\right) ,$ $T\leqq\infty,$ where $q>0,$
and $\Omega=\mathbb{R}^{N},$ or $\Omega$ is a smooth bounded domain of
$\mathbb{R}^{N}$ and $u=0$ on $\partial\Omega\times\left( 0,T\right) .$ We can
define the trace at $t=0$ as a nonnegative Borel measure $(\mathcal{S}
,u\_{0}),$ where $S$ is the closed set where it is infinite, and $u\_{0}$ is a
Radon measure on $\Omega\backslash\mathcal{S}.$ We show that the trace is a
Radon measure when $q\leqq1.$ For $q\in(1,(N+2)/(N+1)$ and any given Borel
measure, we show the existence of a minimal solution, and a maximal one on
conditions on $u\_{0}.$ When $\mathcal{S}$ $=\overline{\omega}\cap\Omega$ and
$\omega$ is an open subset of $\Omega,$ the existence extends to any $q\leqq2$
when $u\_{0}\in L\_{loc}^{1}(\Omega)$ and any $q>1$ when $u\_{0}=0$. In
particular there exists a self-similar nonradial solution with trace
$(\mathbb{R}^{N+},0),$ with a growth rate of order $\left\vert x\right\vert
^{q^{\prime}}$ as $\left\vert x\right\vert \rightarrow\infty$ for fixed $t.$
Moreover we show that the solutions with trace $(\overline{\omega},0)$ in
$Q\_{\mathbb{R}^{N},T}$ may present near $t=0$ a growth rate of order
$t^{-1/(q-1)}$ in $\omega$ and of order $t^{-(2-q)/(q-1)}$ on $\partial
\omega.$

Analysis of PDEs